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

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


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

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

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

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

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

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

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

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

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

Solving
-2 + 1x + x2 = -6 + 3x + 3x2

Solving for variable 'x'.

Reorder the terms:
-2 + 6 + 1x + -3x + x2 + -3x2 = -6 + 3x + 3x2 + 6 + -3x + -3x2

Combine like terms: -2 + 6 = 4
4 + 1x + -3x + x2 + -3x2 = -6 + 3x + 3x2 + 6 + -3x + -3x2

Combine like terms: 1x + -3x = -2x
4 + -2x + x2 + -3x2 = -6 + 3x + 3x2 + 6 + -3x + -3x2

Combine like terms: x2 + -3x2 = -2x2
4 + -2x + -2x2 = -6 + 3x + 3x2 + 6 + -3x + -3x2

Reorder the terms:
4 + -2x + -2x2 = -6 + 6 + 3x + -3x + 3x2 + -3x2

Combine like terms: -6 + 6 = 0
4 + -2x + -2x2 = 0 + 3x + -3x + 3x2 + -3x2
4 + -2x + -2x2 = 3x + -3x + 3x2 + -3x2

Combine like terms: 3x + -3x = 0
4 + -2x + -2x2 = 0 + 3x2 + -3x2
4 + -2x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
4 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -1x + -1x2) = 0

Factor a trinomial.
2((1 + -1x)(2 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1

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 = {1, -2}

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