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

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


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

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

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

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

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

Solving
40 = 4 + 6x + 2x2

Solving for variable 'x'.

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

Reorder the terms:
36 + -6x + -2x2 = 4 + -4 + 6x + -6x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
36 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2
36 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -3x + -1x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {3, -6}

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