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

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


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

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

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

Multiply (-1 + 3x) * (2 + x)
(-1(2 + x) + 3x * (2 + x)) = 2(x + -1)
((2 * -1 + x * -1) + 3x * (2 + x)) = 2(x + -1)
((-2 + -1x) + 3x * (2 + x)) = 2(x + -1)
(-2 + -1x + (2 * 3x + x * 3x)) = 2(x + -1)
(-2 + -1x + (6x + 3x2)) = 2(x + -1)

Combine like terms: -1x + 6x = 5x
(-2 + 5x + 3x2) = 2(x + -1)

Reorder the terms:
-2 + 5x + 3x2 = 2(-1 + x)
-2 + 5x + 3x2 = (-1 * 2 + x * 2)
-2 + 5x + 3x2 = (-2 + 2x)

Add '2' to each side of the equation.
-2 + 5x + 2 + 3x2 = -2 + 2 + 2x

Reorder the terms:
-2 + 2 + 5x + 3x2 = -2 + 2 + 2x

Combine like terms: -2 + 2 = 0
0 + 5x + 3x2 = -2 + 2 + 2x
5x + 3x2 = -2 + 2 + 2x

Combine like terms: -2 + 2 = 0
5x + 3x2 = 0 + 2x
5x + 3x2 = 2x

Solving
5x + 3x2 = 2x

Solving for variable 'x'.

Reorder the terms:
5x + -2x + 3x2 = 2x + -2x

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

Combine like terms: 2x + -2x = 0
3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {0, -1}

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