(2+2x)(4+2x)=15

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Solution for (2+2x)(4+2x)=15 equation: 


Simplifying
(2 + 2x)(4 + 2x) = 15

Multiply (2 + 2x) * (4 + 2x)
(2(4 + 2x) + 2x * (4 + 2x)) = 15
((4 * 2 + 2x * 2) + 2x * (4 + 2x)) = 15
((8 + 4x) + 2x * (4 + 2x)) = 15
(8 + 4x + (4 * 2x + 2x * 2x)) = 15
(8 + 4x + (8x + 4x2)) = 15

Combine like terms: 4x + 8x = 12x
(8 + 12x + 4x2) = 15

Solving
8 + 12x + 4x2 = 15

Solving for variable 'x'.

Reorder the terms:
8 + -15 + 12x + 4x2 = 15 + -15

Combine like terms: 8 + -15 = -7
-7 + 12x + 4x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-7 + 12x + 4x2 = 0

Factor a trinomial.
(-7 + -2x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-3.5, 0.5}

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