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

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


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

Reorder the terms:
2x(1 + x) = x(x + -3)
(1 * 2x + x * 2x) = x(x + -3)
(2x + 2x2) = x(x + -3)

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

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

Solving for variable 'x'.

Reorder the terms:
2x + 3x + 2x2 + -1x2 = -3x + x2 + 3x + -1x2

Combine like terms: 2x + 3x = 5x
5x + 2x2 + -1x2 = -3x + x2 + 3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
5x + 1x2 = -3x + x2 + 3x + -1x2

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

Combine like terms: -3x + 3x = 0
5x + 1x2 = 0 + x2 + -1x2
5x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {0, -5}

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