9x^2+36x+36=15x^2-31x-24

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Solution for 9x^2+36x+36=15x^2-31x-24 equation: 


Simplifying
9x2 + 36x + 36 = 15x2 + -31x + -24

Reorder the terms:
36 + 36x + 9x2 = 15x2 + -31x + -24

Reorder the terms:
36 + 36x + 9x2 = -24 + -31x + 15x2

Solving
36 + 36x + 9x2 = -24 + -31x + 15x2

Solving for variable 'x'.

Reorder the terms:
36 + 24 + 36x + 31x + 9x2 + -15x2 = -24 + -31x + 15x2 + 24 + 31x + -15x2

Combine like terms: 36 + 24 = 60
60 + 36x + 31x + 9x2 + -15x2 = -24 + -31x + 15x2 + 24 + 31x + -15x2

Combine like terms: 36x + 31x = 67x
60 + 67x + 9x2 + -15x2 = -24 + -31x + 15x2 + 24 + 31x + -15x2

Combine like terms: 9x2 + -15x2 = -6x2
60 + 67x + -6x2 = -24 + -31x + 15x2 + 24 + 31x + -15x2

Reorder the terms:
60 + 67x + -6x2 = -24 + 24 + -31x + 31x + 15x2 + -15x2

Combine like terms: -24 + 24 = 0
60 + 67x + -6x2 = 0 + -31x + 31x + 15x2 + -15x2
60 + 67x + -6x2 = -31x + 31x + 15x2 + -15x2

Combine like terms: -31x + 31x = 0
60 + 67x + -6x2 = 0 + 15x2 + -15x2
60 + 67x + -6x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
60 + 67x + -6x2 = 0

Factor a trinomial.
(12 + -1x)(5 + 6x) = 0


Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

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

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

Divide each side by '-1'.
x = 12

Simplifying
x = 12

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

Simplifying
5 + 6x = 0

Solving
5 + 6x = 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 + 6x = 0 + -5

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

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

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {12, -0.8333333333}

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