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

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


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

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

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

Multiply (2 + x) * (-5 + x)
(2(-5 + x) + x(-5 + x)) = 2 + -2x
((-5 * 2 + x * 2) + x(-5 + x)) = 2 + -2x
((-10 + 2x) + x(-5 + x)) = 2 + -2x
(-10 + 2x + (-5 * x + x * x)) = 2 + -2x
(-10 + 2x + (-5x + x2)) = 2 + -2x

Combine like terms: 2x + -5x = -3x
(-10 + -3x + x2) = 2 + -2x

Solving
-10 + -3x + x2 = 2 + -2x

Solving for variable 'x'.

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

Combine like terms: -10 + -2 = -12
-12 + -3x + 2x + x2 = 2 + -2x + -2 + 2x

Combine like terms: -3x + 2x = -1x
-12 + -1x + x2 = 2 + -2x + -2 + 2x

Reorder the terms:
-12 + -1x + x2 = 2 + -2 + -2x + 2x

Combine like terms: 2 + -2 = 0
-12 + -1x + x2 = 0 + -2x + 2x
-12 + -1x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -1x) = 0


Subproblem 1
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

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 = {-3, 4}

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