(x+2)*(x-6)=84

Solution for (x+2)*(x-6)=84 equation:

Simplifying
(x + 2)(x + -6) = 84

Reorder the terms:
(2 + x)(x + -6) = 84

Reorder the terms:
(2 + x)(-6 + x) = 84

Multiply (2 + x) * (-6 + x)
(2(-6 + x) + x(-6 + x)) = 84
((-6 * 2 + x * 2) + x(-6 + x)) = 84
((-12 + 2x) + x(-6 + x)) = 84
(-12 + 2x + (-6 * x + x * x)) = 84
(-12 + 2x + (-6x + x2)) = 84

Combine like terms: 2x + -6x = -4x
(-12 + -4x + x2) = 84

Solving
-12 + -4x + x2 = 84

Solving for variable 'x'.

Reorder the terms:
-12 + -84 + -4x + x2 = 84 + -84

Combine like terms: -12 + -84 = -96
-96 + -4x + x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-96 + -4x + x2 = 0

Factor a trinomial.
(-8 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-8, 12}