Solve by Factoring -25x^2+300x=0

$- 25 x^{2} + 300 x = 0$

Step 1

Factor $25 x$ out of $- 25 x^{2} + 300 x$ .

Factor $25 x$ out of $- 25 x^{2}$ .

$25 x (- x) + 300 x = 0$

Factor $25 x$ out of $300 x$ .

$25 x (- x) + 25 x (12) = 0$

Factor $25 x$ out of $25 x (- x) + 25 x (12)$ .

$25 x (- x + 12) = 0$

Step 2

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

$x = 0$

$- x + 12 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $- x + 12$ equal to $0$ and solve for $x$ .

Set $- x + 12$ equal to $0$ .

$- x + 12 = 0$

Solve $- x + 12 = 0$ for $x$ .

Subtract $12$ from both sides of the equation.

$- x = - 12$

Divide each term in $- x = - 12$ by $- 1$ and simplify.

Divide each term in $- x = - 12$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 12}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 12}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 1}$

Simplify the right side.

Divide $- 12$ by $- 1$ .

$x = 12$

Step 5

The final solution is all the values that make $25 x (- x + 12) = 0$ true.

$x = 0, 12$