(x+2)(x+8)=72

Solution for (x+2)(x+8)=72 equation:

Simplifying
(x + 2)(x + 8) = 72

Reorder the terms:
(2 + x)(x + 8) = 72

Reorder the terms:
(2 + x)(8 + x) = 72

Multiply (2 + x) * (8 + x)
(2(8 + x) + x(8 + x)) = 72
((8 * 2 + x * 2) + x(8 + x)) = 72
((16 + 2x) + x(8 + x)) = 72
(16 + 2x + (8 * x + x * x)) = 72
(16 + 2x + (8x + x2)) = 72

Combine like terms: 2x + 8x = 10x
(16 + 10x + x2) = 72

Solving
16 + 10x + x2 = 72

Solving for variable 'x'.

Reorder the terms:
16 + -72 + 10x + x2 = 72 + -72

Combine like terms: 16 + -72 = -56
-56 + 10x + x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-56 + 10x + x2 = 0

Factor a trinomial.
(-14 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-14, 4}