(2x+2)(x+2)=40

Solution for (2x+2)(x+2)=40 equation:

Simplifying
(2x + 2)(x + 2) = 40

Reorder the terms:
(2 + 2x)(x + 2) = 40

Reorder the terms:
(2 + 2x)(2 + x) = 40

Multiply (2 + 2x) * (2 + x)
(2(2 + x) + 2x * (2 + x)) = 40
((2 * 2 + x * 2) + 2x * (2 + x)) = 40
((4 + 2x) + 2x * (2 + x)) = 40
(4 + 2x + (2 * 2x + x * 2x)) = 40
(4 + 2x + (4x + 2x2)) = 40

Combine like terms: 2x + 4x = 6x
(4 + 6x + 2x2) = 40

Solving
4 + 6x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
4 + -40 + 6x + 2x2 = 40 + -40

Combine like terms: 4 + -40 = -36
-36 + 6x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-36 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 3x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-6, 3}