(x+5)(x-4)=52

Solution for (x+5)(x-4)=52 equation:

Simplifying
(x + 5)(x + -4) = 52

Reorder the terms:
(5 + x)(x + -4) = 52

Reorder the terms:
(5 + x)(-4 + x) = 52

Multiply (5 + x) * (-4 + x)
(5(-4 + x) + x(-4 + x)) = 52
((-4 * 5 + x * 5) + x(-4 + x)) = 52
((-20 + 5x) + x(-4 + x)) = 52
(-20 + 5x + (-4 * x + x * x)) = 52
(-20 + 5x + (-4x + x2)) = 52

Combine like terms: 5x + -4x = 1x
(-20 + 1x + x2) = 52

Solving
-20 + 1x + x2 = 52

Solving for variable 'x'.

Reorder the terms:
-20 + -52 + 1x + x2 = 52 + -52

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

Combine like terms: 52 + -52 = 0
-72 + 1x + x2 = 0

Factor a trinomial.
(-9 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-9, 8}