(x-1)(x+2)=5(x-1)

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Solution for (x-1)(x+2)=5(x-1) equation: 


Simplifying
(x + -1)(x + 2) = 5(x + -1)

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

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

Multiply (-1 + x) * (2 + x)
(-1(2 + x) + x(2 + x)) = 5(x + -1)
((2 * -1 + x * -1) + x(2 + x)) = 5(x + -1)
((-2 + -1x) + x(2 + x)) = 5(x + -1)
(-2 + -1x + (2 * x + x * x)) = 5(x + -1)
(-2 + -1x + (2x + x2)) = 5(x + -1)

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

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

Solving
-2 + 1x + x2 = -5 + 5x

Solving for variable 'x'.

Reorder the terms:
-2 + 5 + 1x + -5x + x2 = -5 + 5x + 5 + -5x

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

Combine like terms: 1x + -5x = -4x
3 + -4x + x2 = -5 + 5x + 5 + -5x

Reorder the terms:
3 + -4x + x2 = -5 + 5 + 5x + -5x

Combine like terms: -5 + 5 = 0
3 + -4x + x2 = 0 + 5x + -5x
3 + -4x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
3 + -4x + x2 = 0

Factor a trinomial.
(1 + -1x)(3 + -1x) = 0


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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}

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