(3x)*(3x+3)*2=(5x-1)*(3x)

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Solution for (3x)*(3x+3)*2=(5x-1)*(3x) equation: 


Simplifying
(3x)(3x + 3) * 2 = (5x + -1)(3x)

Remove parenthesis around (3x)
3x(3x + 3) * 2 = (5x + -1)(3x)

Reorder the terms:
3x(3 + 3x) * 2 = (5x + -1)(3x)

Reorder the terms for easier multiplication:
3 * 2x(3 + 3x) = (5x + -1)(3x)

Multiply 3 * 2
6x(3 + 3x) = (5x + -1)(3x)
(3 * 6x + 3x * 6x) = (5x + -1)(3x)
(18x + 18x2) = (5x + -1)(3x)

Reorder the terms:
18x + 18x2 = (-1 + 5x)(3x)

Remove parenthesis around (3x)
18x + 18x2 = (-1 + 5x) * 3x

Reorder the terms for easier multiplication:
18x + 18x2 = 3x(-1 + 5x)
18x + 18x2 = (-1 * 3x + 5x * 3x)
18x + 18x2 = (-3x + 15x2)

Solving
18x + 18x2 = -3x + 15x2

Solving for variable 'x'.

Reorder the terms:
18x + 3x + 18x2 + -15x2 = -3x + 15x2 + 3x + -15x2

Combine like terms: 18x + 3x = 21x
21x + 18x2 + -15x2 = -3x + 15x2 + 3x + -15x2

Combine like terms: 18x2 + -15x2 = 3x2
21x + 3x2 = -3x + 15x2 + 3x + -15x2

Reorder the terms:
21x + 3x2 = -3x + 3x + 15x2 + -15x2

Combine like terms: -3x + 3x = 0
21x + 3x2 = 0 + 15x2 + -15x2
21x + 3x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(7 + x) = 0

Ignore the factor 3.

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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {0, -7}

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