7x^2+3x-12=36-31x

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Solution for 7x^2+3x-12=36-31x equation: 


Simplifying
7x2 + 3x + -12 = 36 + -31x

Reorder the terms:
-12 + 3x + 7x2 = 36 + -31x

Solving
-12 + 3x + 7x2 = 36 + -31x

Solving for variable 'x'.

Reorder the terms:
-12 + -36 + 3x + 31x + 7x2 = 36 + -31x + -36 + 31x

Combine like terms: -12 + -36 = -48
-48 + 3x + 31x + 7x2 = 36 + -31x + -36 + 31x

Combine like terms: 3x + 31x = 34x
-48 + 34x + 7x2 = 36 + -31x + -36 + 31x

Reorder the terms:
-48 + 34x + 7x2 = 36 + -36 + -31x + 31x

Combine like terms: 36 + -36 = 0
-48 + 34x + 7x2 = 0 + -31x + 31x
-48 + 34x + 7x2 = -31x + 31x

Combine like terms: -31x + 31x = 0
-48 + 34x + 7x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -7x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143
Solution
x = {-6, 1.142857143}

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