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

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


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

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

Remove parenthesis around (2x)
(3 + 2x) * 2x(2x + 2) = (2x)(2x)(3x + 3)

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

Reorder the terms for easier multiplication:
2x(3 + 2x)(2 + 2x) = (2x)(2x)(3x + 3)

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

Combine like terms: 6x + 4x = 10x
2x(6 + 10x + 4x2) = (2x)(2x)(3x + 3)
(6 * 2x + 10x * 2x + 4x2 * 2x) = (2x)(2x)(3x + 3)
(12x + 20x2 + 8x3) = (2x)(2x)(3x + 3)

Remove parenthesis around (2x)
12x + 20x2 + 8x3 = 2x(2x)(3x + 3)

Remove parenthesis around (2x)
12x + 20x2 + 8x3 = 2x * 2x(3x + 3)

Reorder the terms:
12x + 20x2 + 8x3 = 2x * 2x(3 + 3x)

Reorder the terms for easier multiplication:
12x + 20x2 + 8x3 = 2 * 2x * x(3 + 3x)

Multiply 2 * 2
12x + 20x2 + 8x3 = 4x * x(3 + 3x)

Multiply x * x
12x + 20x2 + 8x3 = 4x2(3 + 3x)
12x + 20x2 + 8x3 = (3 * 4x2 + 3x * 4x2)
12x + 20x2 + 8x3 = (12x2 + 12x3)

Solving
12x + 20x2 + 8x3 = 12x2 + 12x3

Solving for variable 'x'.

Reorder the terms:
12x + 20x2 + -12x2 + 8x3 + -12x3 = 12x2 + 12x3 + -12x2 + -12x3

Combine like terms: 20x2 + -12x2 = 8x2
12x + 8x2 + 8x3 + -12x3 = 12x2 + 12x3 + -12x2 + -12x3

Combine like terms: 8x3 + -12x3 = -4x3
12x + 8x2 + -4x3 = 12x2 + 12x3 + -12x2 + -12x3

Reorder the terms:
12x + 8x2 + -4x3 = 12x2 + -12x2 + 12x3 + -12x3

Combine like terms: 12x2 + -12x2 = 0
12x + 8x2 + -4x3 = 0 + 12x3 + -12x3
12x + 8x2 + -4x3 = 12x3 + -12x3

Combine like terms: 12x3 + -12x3 = 0
12x + 8x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(3 + 2x + -1x2) = 0

Factor a trinomial.
4x((3 + -1x)(1 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {0, 3, -1}

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