(x-8)(x+6)=32

Solution for (x-8)(x+6)=32 equation:

Simplifying
(x + -8)(x + 6) = 32

Reorder the terms:
(-8 + x)(x + 6) = 32

Reorder the terms:
(-8 + x)(6 + x) = 32

Multiply (-8 + x) * (6 + x)
(-8(6 + x) + x(6 + x)) = 32
((6 * -8 + x * -8) + x(6 + x)) = 32
((-48 + -8x) + x(6 + x)) = 32
(-48 + -8x + (6 * x + x * x)) = 32
(-48 + -8x + (6x + x2)) = 32

Combine like terms: -8x + 6x = -2x
(-48 + -2x + x2) = 32

Solving
-48 + -2x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
-48 + -32 + -2x + x2 = 32 + -32

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

Combine like terms: 32 + -32 = 0
-80 + -2x + x2 = 0

Factor a trinomial.
(-8 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-8, 10}