5x^2+8x-14=40-31x

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Solution for 5x^2+8x-14=40-31x equation: 


Simplifying
5x2 + 8x + -14 = 40 + -31x

Reorder the terms:
-14 + 8x + 5x2 = 40 + -31x

Solving
-14 + 8x + 5x2 = 40 + -31x

Solving for variable 'x'.

Reorder the terms:
-14 + -40 + 8x + 31x + 5x2 = 40 + -31x + -40 + 31x

Combine like terms: -14 + -40 = -54
-54 + 8x + 31x + 5x2 = 40 + -31x + -40 + 31x

Combine like terms: 8x + 31x = 39x
-54 + 39x + 5x2 = 40 + -31x + -40 + 31x

Reorder the terms:
-54 + 39x + 5x2 = 40 + -40 + -31x + 31x

Combine like terms: 40 + -40 = 0
-54 + 39x + 5x2 = 0 + -31x + 31x
-54 + 39x + 5x2 = -31x + 31x

Combine like terms: -31x + 31x = 0
-54 + 39x + 5x2 = 0

Factor a trinomial.
(-9 + -1x)(6 + -5x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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 = {-9, 1.2}

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