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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: 2x + 6x = 8x
8x + x2 + -2x2 = -6x + 2x2 + 6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
8x + -1x2 = -6x + 2x2 + 6x + -2x2

Reorder the terms:
8x + -1x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
8x + -1x2 = 0 + 2x2 + -2x2
8x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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