x(x+2)=4x(x+2)

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Solution for x(x+2)=4x(x+2) equation: 


Simplifying
x(x + 2) = 4x(x + 2)

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

Reorder the terms:
2x + x2 = 4x(2 + x)
2x + x2 = (2 * 4x + x * 4x)
2x + x2 = (8x + 4x2)

Solving
2x + x2 = 8x + 4x2

Solving for variable 'x'.

Reorder the terms:
2x + -8x + x2 + -4x2 = 8x + 4x2 + -8x + -4x2

Combine like terms: 2x + -8x = -6x
-6x + x2 + -4x2 = 8x + 4x2 + -8x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-6x + -3x2 = 8x + 4x2 + -8x + -4x2

Reorder the terms:
-6x + -3x2 = 8x + -8x + 4x2 + -4x2

Combine like terms: 8x + -8x = 0
-6x + -3x2 = 0 + 4x2 + -4x2
-6x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3x'.
-3x(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0, -2}

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