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

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


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

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

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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: -2x + 2x = 0
-2 + 1x + x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-2, 1}

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