(x+2)(x-1)=-2(x-4)

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Solution for (x+2)(x-1)=-2(x-4) equation: 


Simplifying
(x + 2)(x + -1) = -2(x + -4)

Reorder the terms:
(2 + x)(x + -1) = -2(x + -4)

Reorder the terms:
(2 + x)(-1 + x) = -2(x + -4)

Multiply (2 + x) * (-1 + x)
(2(-1 + x) + x(-1 + x)) = -2(x + -4)
((-1 * 2 + x * 2) + x(-1 + x)) = -2(x + -4)
((-2 + 2x) + x(-1 + x)) = -2(x + -4)
(-2 + 2x + (-1 * x + x * x)) = -2(x + -4)
(-2 + 2x + (-1x + x2)) = -2(x + -4)

Combine like terms: 2x + -1x = 1x
(-2 + 1x + x2) = -2(x + -4)

Reorder the terms:
-2 + 1x + x2 = -2(-4 + x)
-2 + 1x + x2 = (-4 * -2 + x * -2)
-2 + 1x + x2 = (8 + -2x)

Solving
-2 + 1x + x2 = 8 + -2x

Solving for variable 'x'.

Reorder the terms:
-2 + -8 + 1x + 2x + x2 = 8 + -2x + -8 + 2x

Combine like terms: -2 + -8 = -10
-10 + 1x + 2x + x2 = 8 + -2x + -8 + 2x

Combine like terms: 1x + 2x = 3x
-10 + 3x + x2 = 8 + -2x + -8 + 2x

Reorder the terms:
-10 + 3x + x2 = 8 + -8 + -2x + 2x

Combine like terms: 8 + -8 = 0
-10 + 3x + x2 = 0 + -2x + 2x
-10 + 3x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-10 + 3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

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

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

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}

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