Solve by Factoring 12x^2+13x=5x

$12 x^{2} + 13 x = 5 x$

Step 1

Subtract $5 x$ from both sides of the equation.

$12 x^{2} + 13 x - 5 x = 0$

Step 2

Subtract $5 x$ from $13 x$ .

$12 x^{2} + 8 x = 0$

Step 3

Factor $4 x$ out of $12 x^{2} + 8 x$ .

Factor $4 x$ out of $12 x^{2}$ .

$4 x (3 x) + 8 x = 0$

Factor $4 x$ out of $8 x$ .

$4 x (3 x) + 4 x (2) = 0$

Factor $4 x$ out of $4 x (3 x) + 4 x (2)$ .

$4 x (3 x + 2) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$3 x + 2 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $3 x + 2$ equal to $0$ and solve for $x$ .

Set $3 x + 2$ equal to $0$ .

$3 x + 2 = 0$

Solve $3 x + 2 = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$3 x = - 2$

Divide each term in $3 x = - 2$ by $3$ and simplify.

Divide each term in $3 x = - 2$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 7

The final solution is all the values that make $4 x (3 x + 2) = 0$ true.

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