# How do you factor 3x^2 = 16x +12?

Feb 5, 2017

Factored is $\left(3 x + 2\right) \left(x - 6\right) = 0$
Solved is $x = - \frac{2}{3}$ or $x = 6$

#### Explanation:

$3 {x}^{2} = 16 x + 12$

Subtract $\left(16 x + 12\right)$ from each side.

$3 {x}^{2} - \left(16 x + 12\right) = 0$

Open the brackets and simplify. The product of a negative and a positive is a negative.

$3 {x}^{2} - 16 x - 12 = 0$

Factorise.

$3 {x}^{2} - 18 x + 2 x - 12 = 0$

$3 x \left(x - 6\right) + 2 \left(x - 6\right) = 0$

$\left(3 x + 2\right) \left(x - 6\right) = 0$

$3 x + 2 = 0$ or $x - 6 = 0$

$x = - \frac{2}{3}$ or $x = 6$

Feb 5, 2017

$\left(3 x + 2\right) \left(x - 6\right)$

#### Explanation:

First, get all the terms to one side: $3 {x}^{2} - 16 x - 12 = 0.$
Since there is no greatest common factor, then you would need to factor by guessing and checking.

Start off by setting up two quantities (3x +- ?) and (x +- ?), since you know that once you FOIL these two binomials, they must start with $3 {x}^{2}$.

Then think about which two numbers you can multiply that equals to 12. It's either: 1 and 12, 3 and 4, or 2 and 6. Substitute these pairs of numbers into the ? and FOIL to see which pair of numbers work. However, you would also need to check whether you need to add or subtract one of the numbers in the pairs, since the signs are unknown.

Once you have tried all three pairs, you should know that 2 and 6 works, and that you are adding 2 to $3 x$ and subtracting 6 from $x$. Therefore, your factors are: $\left(3 x + 2\right) \left(x - 6\right)$.

There are probably better ways to factor, but this is how I factor my equations.