3x^2-9x-22=2x+12

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Solution for 3x^2-9x-22=2x+12 equation: 


Simplifying
3x2 + -9x + -22 = 2x + 12

Reorder the terms:
-22 + -9x + 3x2 = 2x + 12

Reorder the terms:
-22 + -9x + 3x2 = 12 + 2x

Solving
-22 + -9x + 3x2 = 12 + 2x

Solving for variable 'x'.

Reorder the terms:
-22 + -12 + -9x + -2x + 3x2 = 12 + 2x + -12 + -2x

Combine like terms: -22 + -12 = -34
-34 + -9x + -2x + 3x2 = 12 + 2x + -12 + -2x

Combine like terms: -9x + -2x = -11x
-34 + -11x + 3x2 = 12 + 2x + -12 + -2x

Reorder the terms:
-34 + -11x + 3x2 = 12 + -12 + 2x + -2x

Combine like terms: 12 + -12 = 0
-34 + -11x + 3x2 = 0 + 2x + -2x
-34 + -11x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-34 + -11x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(17 + -3x) = 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 '(17 + -3x)' equal to zero and attempt to solve:

Simplifying
17 + -3x = 0

Solving
17 + -3x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -3x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -3x = 0 + -17
-3x = 0 + -17

Combine like terms: 0 + -17 = -17
-3x = -17

Divide each side by '-3'.
x = 5.666666667

Simplifying
x = 5.666666667
Solution
x = {-2, 5.666666667}

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