# How do you solve 4x^2+6x=0 by factoring?

$x = 0 , - \frac{3}{2}$

#### Explanation:

Notice that we can factor out $2 x$ from both terms on the LH side:

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

$\therefore 2 x = 0 , 2 x + 3 = 0$

For 2x=0=>color(blue)(bar(ul(abs(color(black)(x=0

For $2 x + 3 = 0$

2x=-3=>color(blue)(bar(ul(abs(color(black)(x=-3/2

We can see these in the graph:

graph{4x^2+6x}

Jun 28, 2018

$x = 0$, $- \frac{3}{2}$

#### Explanation:

Solve:

$4 {x}^{2} + 6 x = 0$

The greatest common factor of $4$ and $6$ is $2$. The greatest common factor of ${x}^{2}$ and $x$ is $x$. The greatest common factor is $2 x$. Factor out $2 x$.

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

$2 x = 0$

$x = \frac{0}{2}$

$x = 0$

$2 x + 3 = 0$

$2 x = - 3$

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

Solutions for $x$.

$x = 0$, $- \frac{3}{2}$