(x+10)(x-8)=-32

Solution for (x+10)(x-8)=-32 equation:

Simplifying
(x + 10)(x + -8) = -32

Reorder the terms:
(10 + x)(x + -8) = -32

Reorder the terms:
(10 + x)(-8 + x) = -32

Multiply (10 + x) * (-8 + x)
(10(-8 + x) + x(-8 + x)) = -32
((-8 * 10 + x * 10) + x(-8 + x)) = -32
((-80 + 10x) + x(-8 + x)) = -32
(-80 + 10x + (-8 * x + x * x)) = -32
(-80 + 10x + (-8x + x2)) = -32

Combine like terms: 10x + -8x = 2x
(-80 + 2x + x2) = -32

Solving
-80 + 2x + x2 = -32

Solving for variable 'x'.

Reorder the terms:
-80 + 32 + 2x + x2 = -32 + 32

Combine like terms: -80 + 32 = -48
-48 + 2x + x2 = -32 + 32

Combine like terms: -32 + 32 = 0
-48 + 2x + x2 = 0

Factor a trinomial.
(-8 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-8, 6}