(x-5)(x+9)=32

Solution for (x-5)(x+9)=32 equation:

Simplifying
(x + -5)(x + 9) = 32

Reorder the terms:
(-5 + x)(x + 9) = 32

Reorder the terms:
(-5 + x)(9 + x) = 32

Multiply (-5 + x) * (9 + x)
(-5(9 + x) + x(9 + x)) = 32
((9 * -5 + x * -5) + x(9 + x)) = 32
((-45 + -5x) + x(9 + x)) = 32
(-45 + -5x + (9 * x + x * x)) = 32
(-45 + -5x + (9x + x2)) = 32

Combine like terms: -5x + 9x = 4x
(-45 + 4x + x2) = 32

Solving
-45 + 4x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
-45 + -32 + 4x + x2 = 32 + -32

Combine like terms: -45 + -32 = -77
-77 + 4x + x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-77 + 4x + x2 = 0

Factor a trinomial.
(-11 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-11, 7}