2x(x+6)=x(3x-3)

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Solution for 2x(x+6)=x(3x-3) equation: 


Simplifying
2x(x + 6) = x(3x + -3)

Reorder the terms:
2x(6 + x) = x(3x + -3)
(6 * 2x + x * 2x) = x(3x + -3)
(12x + 2x2) = x(3x + -3)

Reorder the terms:
12x + 2x2 = x(-3 + 3x)
12x + 2x2 = (-3 * x + 3x * x)
12x + 2x2 = (-3x + 3x2)

Solving
12x + 2x2 = -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
12x + 3x + 2x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 12x + 3x = 15x
15x + 2x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
15x + -1x2 = -3x + 3x2 + 3x + -3x2

Reorder the terms:
15x + -1x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
15x + -1x2 = 0 + 3x2 + -3x2
15x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
15x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -1x) = 0


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 '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {0, 15}

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