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

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


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

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

Reorder the terms:
6x + 3x2 = 2x(-2 + x)
6x + 3x2 = (-2 * 2x + x * 2x)
6x + 3x2 = (-4x + 2x2)

Solving
6x + 3x2 = -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
6x + 4x + 3x2 + -2x2 = -4x + 2x2 + 4x + -2x2

Combine like terms: 6x + 4x = 10x
10x + 3x2 + -2x2 = -4x + 2x2 + 4x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
10x + 1x2 = -4x + 2x2 + 4x + -2x2

Reorder the terms:
10x + 1x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
10x + 1x2 = 0 + 2x2 + -2x2
10x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {0, -10}

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