Solve by Factoring 20x^2=-25x

$20 x^{2} = - 25 x$

Step 1

Add $25 x$ to both sides of the equation.

$20 x^{2} + 25 x = 0$

Step 2

Factor $5 x$ out of $20 x^{2} + 25 x$ .

Factor $5 x$ out of $20 x^{2}$ .

$5 x (4 x) + 25 x = 0$

Factor $5 x$ out of $25 x$ .

$5 x (4 x) + 5 x (5) = 0$

Factor $5 x$ out of $5 x (4 x) + 5 x (5)$ .

$5 x (4 x + 5) = 0$

Step 3

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

$x = 0$

$4 x + 5 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $4 x + 5$ equal to $0$ and solve for $x$ .

Set $4 x + 5$ equal to $0$ .

$4 x + 5 = 0$

Solve $4 x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$4 x = - 5$

Divide each term in $4 x = - 5$ by $4$ and simplify.

Divide each term in $4 x = - 5$ by $4$ .

$\frac{4 x}{4} = \frac{- 5}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 5}{4}$

Divide $x$ by $1$ .

$x = \frac{- 5}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{4}$

Step 6

The final solution is all the values that make $5 x (4 x + 5) = 0$ true.

$x = 0, - \frac{5}{4}$