(x+8)(x-9)=-52

Solution for (x+8)(x-9)=-52 equation:

Simplifying
(x + 8)(x + -9) = -52

Reorder the terms:
(8 + x)(x + -9) = -52

Reorder the terms:
(8 + x)(-9 + x) = -52

Multiply (8 + x) * (-9 + x)
(8(-9 + x) + x(-9 + x)) = -52
((-9 * 8 + x * 8) + x(-9 + x)) = -52
((-72 + 8x) + x(-9 + x)) = -52
(-72 + 8x + (-9 * x + x * x)) = -52
(-72 + 8x + (-9x + x2)) = -52

Combine like terms: 8x + -9x = -1x
(-72 + -1x + x2) = -52

Solving
-72 + -1x + x2 = -52

Solving for variable 'x'.

Reorder the terms:
-72 + 52 + -1x + x2 = -52 + 52

Combine like terms: -72 + 52 = -20
-20 + -1x + x2 = -52 + 52

Combine like terms: -52 + 52 = 0
-20 + -1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-4, 5}