Solve by Factoring 8x^2+30x=2x

$8 x^{2} + 30 x = 2 x$

Step 1

Subtract $2 x$ from both sides of the equation.

$8 x^{2} + 30 x - 2 x = 0$

Step 2

Subtract $2 x$ from $30 x$ .

$8 x^{2} + 28 x = 0$

Step 3

Factor $4 x$ out of $8 x^{2} + 28 x$ .

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

$4 x (2 x) + 28 x = 0$

Factor $4 x$ out of $28 x$ .

$4 x (2 x) + 4 x (7) = 0$

Factor $4 x$ out of $4 x (2 x) + 4 x (7)$ .

$4 x (2 x + 7) = 0$

Step 4

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

$x = 0$

$2 x + 7 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $2 x + 7$ equal to $0$ and solve for $x$ .

Set $2 x + 7$ equal to $0$ .

$2 x + 7 = 0$

Solve $2 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$2 x = - 7$

Divide each term in $2 x = - 7$ by $2$ and simplify.

Divide each term in $2 x = - 7$ by $2$ .

$\frac{2 x}{2} = \frac{- 7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 7}{2}$

Divide $x$ by $1$ .

$x = \frac{- 7}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Step 7

The final solution is all the values that make $4 x (2 x + 7) = 0$ true.

$x = 0, - \frac{7}{2}$