(2x+2)(2x+3)=72

Solution for (2x+2)(2x+3)=72 equation:

Simplifying
(2x + 2)(2x + 3) = 72

Reorder the terms:
(2 + 2x)(2x + 3) = 72

Reorder the terms:
(2 + 2x)(3 + 2x) = 72

Multiply (2 + 2x) * (3 + 2x)
(2(3 + 2x) + 2x * (3 + 2x)) = 72
((3 * 2 + 2x * 2) + 2x * (3 + 2x)) = 72
((6 + 4x) + 2x * (3 + 2x)) = 72
(6 + 4x + (3 * 2x + 2x * 2x)) = 72
(6 + 4x + (6x + 4x2)) = 72

Combine like terms: 4x + 6x = 10x
(6 + 10x + 4x2) = 72

Solving
6 + 10x + 4x2 = 72

Solving for variable 'x'.

Reorder the terms:
6 + -72 + 10x + 4x2 = 72 + -72

Combine like terms: 6 + -72 = -66
-66 + 10x + 4x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-66 + 10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + 5x + 2x2) = 0

Factor a trinomial.
2((-11 + -2x)(3 + -1x)) = 0

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

Simplifying
-11 + -2x = 0

Solving
-11 + -2x = 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 + -2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x = 0 + 11
-2x = 0 + 11

Combine like terms: 0 + 11 = 11
-2x = 11

Divide each side by '-2'.
x = -5.5

Simplifying
x = -5.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-5.5, 3}