# How do you factor 3x^2 - 8x = -4?

Jul 15, 2018

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

#### Explanation:

$\text{add 4 to both sides}$

$3 {x}^{2} - 8 x + 4 = 0 \leftarrow \textcolor{b l u e}{\text{in standard form}}$

$\text{using the a-c method to factor the quadratic}$

$\text{the factors of the product } 3 \times 4 = 12$

$\text{which sum to "-8" are "-6" and } - 2$

$\text{split the middle term using these factors}$

$3 {x}^{2} - 6 x - 2 x + 4 = 0 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$\textcolor{red}{3 x} \left(x - 2\right) \textcolor{red}{- 2} \left(x - 2\right) = 0$

$\text{take out the "color(blue)"common factor } \left(x - 2\right)$

$\left(x - 2\right) \left(\textcolor{red}{3 x - 2}\right) = 0$