Solve by Factoring x^2-5x-13=-5x-4

$x^{2} - 5 x - 13 = - 5 x - 4$

Step 1

Move all the expressions to the left side of the equation.

Add $5 x$ to both sides of the equation.

$x^{2} - 5 x - 13 + 5 x = - 4$

Add $4$ to both sides of the equation.

$x^{2} - 5 x - 13 + 5 x + 4 = 0$

Step 2

Simplify $x^{2} - 5 x - 13 + 5 x + 4$ .

Combine the opposite terms in $x^{2} - 5 x - 13 + 5 x + 4$ .

Add $- 5 x$ and $5 x$ .

$x^{2} + 0 - 13 + 4 = 0$

Add $x^{2}$ and $0$ .

$x^{2} - 13 + 4 = 0$

Add $- 13$ and $4$ .

$x^{2} - 9 = 0$

Step 3

Rewrite $9$ as $3^{2}$ .

$x^{2} - 3^{2} = 0$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$(x + 3) (x - 3) = 0$

Step 5

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

$x + 3 = 0$

$x - 3 = 0$

Step 6

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 7

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Step 8

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

$x = - 3, 3$