# How do you factor completely 3x^2+4x-4+=0?

Jun 30, 2018

$x = - 2$ and $x = \frac{2}{3}$

#### Explanation:

We can use factoring by grouping. Here I will rewrite the $b$ term as the sum of two terms so we can factor.

Our quadratic can be alternatively written as

$\textcolor{t u r q u o i s e}{3 {x}^{2} - 2 x} + \textcolor{\mathmr{and} a n \ge}{6 x - 4} = 0$

We can factor an $x$ out of the light blue term, and a $2$ out of the orange term. This gives us

$\textcolor{t u r q u o i s e}{x \left(3 x - 2\right)} + \textcolor{\mathmr{and} a n \ge}{2 \left(3 x - 2\right)} = 0$

We can factor out a $3 x - 2$ to get

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

Setting both factors equal to zero, we get

$x = - 2$ and $x = \frac{2}{3}$

Hope this helps!