(2x-2)(x+1)=10x-2

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Solution for (2x-2)(x+1)=10x-2 equation: 


Simplifying
(2x + -2)(x + 1) = 10x + -2

Reorder the terms:
(-2 + 2x)(x + 1) = 10x + -2

Reorder the terms:
(-2 + 2x)(1 + x) = 10x + -2

Multiply (-2 + 2x) * (1 + x)
(-2(1 + x) + 2x * (1 + x)) = 10x + -2
((1 * -2 + x * -2) + 2x * (1 + x)) = 10x + -2
((-2 + -2x) + 2x * (1 + x)) = 10x + -2
(-2 + -2x + (1 * 2x + x * 2x)) = 10x + -2
(-2 + -2x + (2x + 2x2)) = 10x + -2

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

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

Add '2' to each side of the equation.
-2 + 2 + 2x2 = -2 + 2 + 10x

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

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

Solving
2x2 = 10x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-5 + x) = 0

Ignore the factor 2.

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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