Solve the given quadratic equation by factoring. 3x2+12x=03x^2+12x=03x2+12x=0

x = 0 , x = − 4 x=0,x=-4 x = 0 , x = − 4

Solve the given quadratic equation by factoring. 3 x 2 + 12 x = 0 3x^2+12x=0 3 x 2 + 12 x = 0

Hey, everyone. Here I wanna solve this quadratic equation by factoring, and I have 3x squared plus 12x is equal to 0. So starting with step 1, I wanna go ahead and write my equation in standard form. But all of my terms are already on the same side of the equation in descending order of power, so step 1 is already done and we can move on to step 2, which is to factor our quadratic completely. So here, since I have 3x squared plus 12x equals 0, I can actually just factor out the greatest common factor, the gcf. So between 3x squared, 3x squared is just 3 times x times x, and 12x is 3 times 4 times x, I can go ahead and factor out a 3x from both of these terms. So factoring my 3 x out and just having whatever is left over, I have this x, and then I have a 4 left over. Now nothing else can be factored out from that. There is no other common factor. So these are my two factors, 3x and x+4, and step 2 is done. Now step 3 is to simply set my factors equal to 0. So I first have 3x equals 0, and then I have x plus 4 is equal to 0. So let's go ahead and solve for x here. So if 3 x is equal to 0, if I just divide both sides by 3, I'm just left with x is equal to 0. So this is one of my solutions. And then x+4 equals equals 0. If I subtract 4 from both sides to isolate x, I'm left with x is equal to negative 4 and this is my other solution. So I have my solutions, I've completed step 3. Let's go ahead and make sure that we did this right and check it by plugging it back in. So x equals 0, if I go ahead and plug that in, I get 3 times 0 squared plus 12 times 0 equals 0. Now all of this stuff is just being multiplied by 0, so I know that they just get canceled out. And I end up with a 0 equals 0, which is definitely a true statement. So I know that my first solution, x equals 0, is good. Let's check our second solution, x equals negative 4. So I have 3 times negative 4 squared plus 12 times negative 4 is equal to 0. Now negative 4 squared is just 16, so this is 3 times 16. And then I have 12 times negative 4, which is a negative 48, is equal to 0. Now 3 times 16 is positive 48 and that is minus 48 equals 0. And 48 minus 48 is, of course, 0, which is equal to 0, another true statement. So I know that my other solution is good. And that's all for this one. I'll see you in the next one.

Solve the given quadratic equation by factoring. 3 x 2 + 12 x = 0 3x^2+12x=0 3 x 2 + 12 x = 0

x = 0 , x = − 4 x=0,x=-4 x = 0 , x = − 4

x = 3 , x = 4 x=3,x=4 x = 3 , x = 4

x = − 3 , x = − 4 x=-3,x=-4 x = − 3 , x = − 4

x = 1 , x = 4 x=1,x=4 x = 1 , x = 4

1. Equations and Inequalities

Intro to Quadratic Equations

Precalculus

1. Equations and inequalities

Intro to Quadratic Equations

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Multiple Choice

Solve the given quadratic equation by factoring. $3x^2+12x=0$

$x=3,x=4$

$x=0,x=-4$

$x=-3,x=-4$

$x=1,x=4$

Verified step by step guidance

Start by writing the quadratic equation in standard form: $3x^2 + 12x = 0$.

Factor out the greatest common factor from the terms. In this case, the greatest common factor is 3x, so the equation becomes $3x(x + 4) = 0$.

Apply the Zero Product Property, which states that if a product of factors equals zero, at least one of the factors must be zero. Set each factor equal to zero: $3x = 0$ and $x + 4 = 0$.

Solve each equation separately. For $3x = 0$, divide both sides by 3 to find $x = 0$. For $x + 4 = 0$, subtract 4 from both sides to find $x = -4$.

The solutions to the quadratic equation are $x = 0$ and $x = -4$.

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