Solve by Factoring 8x^2+7x=0

$8 x^{2} + 7 x = 0$

Step 1

Factor $x$ out of $8 x^{2} + 7 x$ .

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

$x (8 x) + 7 x = 0$

Factor $x$ out of $7 x$ .

$x (8 x) + x \cdot 7 = 0$

Factor $x$ out of $x (8 x) + x \cdot 7$ .

$x (8 x + 7) = 0$

Step 2

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

$x = 0$

$8 x + 7 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $8 x + 7$ equal to $0$ and solve for $x$ .

Set $8 x + 7$ equal to $0$ .

$8 x + 7 = 0$

Solve $8 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$8 x = - 7$

Divide each term in $8 x = - 7$ by $8$ and simplify.

Divide each term in $8 x = - 7$ by $8$ .

$\frac{8 x}{8} = \frac{- 7}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 7}{8}$

Divide $x$ by $1$ .

$x = \frac{- 7}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{8}$

Step 5

The final solution is all the values that make $x (8 x + 7) = 0$ true.

$x = 0, - \frac{7}{8}$