5x^2+12x-22=2-2x

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Solution for 5x^2+12x-22=2-2x equation: 


Simplifying
5x2 + 12x + -22 = 2 + -2x

Reorder the terms:
-22 + 12x + 5x2 = 2 + -2x

Solving
-22 + 12x + 5x2 = 2 + -2x

Solving for variable 'x'.

Reorder the terms:
-22 + -2 + 12x + 2x + 5x2 = 2 + -2x + -2 + 2x

Combine like terms: -22 + -2 = -24
-24 + 12x + 2x + 5x2 = 2 + -2x + -2 + 2x

Combine like terms: 12x + 2x = 14x
-24 + 14x + 5x2 = 2 + -2x + -2 + 2x

Reorder the terms:
-24 + 14x + 5x2 = 2 + -2 + -2x + 2x

Combine like terms: 2 + -2 = 0
-24 + 14x + 5x2 = 0 + -2x + 2x
-24 + 14x + 5x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-24 + 14x + 5x2 = 0

Factor a trinomial.
(-4 + -1x)(6 + -5x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-4, 1.2}

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