6x^2+6x-11=31-23x

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Solution for 6x^2+6x-11=31-23x equation: 


Simplifying
6x2 + 6x + -11 = 31 + -23x

Reorder the terms:
-11 + 6x + 6x2 = 31 + -23x

Solving
-11 + 6x + 6x2 = 31 + -23x

Solving for variable 'x'.

Reorder the terms:
-11 + -31 + 6x + 23x + 6x2 = 31 + -23x + -31 + 23x

Combine like terms: -11 + -31 = -42
-42 + 6x + 23x + 6x2 = 31 + -23x + -31 + 23x

Combine like terms: 6x + 23x = 29x
-42 + 29x + 6x2 = 31 + -23x + -31 + 23x

Reorder the terms:
-42 + 29x + 6x2 = 31 + -31 + -23x + 23x

Combine like terms: 31 + -31 = 0
-42 + 29x + 6x2 = 0 + -23x + 23x
-42 + 29x + 6x2 = -23x + 23x

Combine like terms: -23x + 23x = 0
-42 + 29x + 6x2 = 0

Factor a trinomial.
(-6 + -1x)(7 + -6x) = 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 '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-6, 1.166666667}

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