x^2-x-18=-2x+2

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Solution for x^2-x-18=-2x+2 equation: 


Simplifying
x2 + -1x + -18 = -2x + 2

Reorder the terms:
-18 + -1x + x2 = -2x + 2

Reorder the terms:
-18 + -1x + x2 = 2 + -2x

Solving
-18 + -1x + x2 = 2 + -2x

Solving for variable 'x'.

Reorder the terms:
-18 + -2 + -1x + 2x + x2 = 2 + -2x + -2 + 2x

Combine like terms: -18 + -2 = -20
-20 + -1x + 2x + x2 = 2 + -2x + -2 + 2x

Combine like terms: -1x + 2x = 1x
-20 + 1x + x2 = 2 + -2x + -2 + 2x

Reorder the terms:
-20 + 1x + x2 = 2 + -2 + -2x + 2x

Combine like terms: 2 + -2 = 0
-20 + 1x + x2 = 0 + -2x + 2x
-20 + 1x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-20 + 1x + x2 = 0

Factor a trinomial.
(-5 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}

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