5x^2+7x-17=31-27x

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Solution for 5x^2+7x-17=31-27x equation: 


Simplifying
5x2 + 7x + -17 = 31 + -27x

Reorder the terms:
-17 + 7x + 5x2 = 31 + -27x

Solving
-17 + 7x + 5x2 = 31 + -27x

Solving for variable 'x'.

Reorder the terms:
-17 + -31 + 7x + 27x + 5x2 = 31 + -27x + -31 + 27x

Combine like terms: -17 + -31 = -48
-48 + 7x + 27x + 5x2 = 31 + -27x + -31 + 27x

Combine like terms: 7x + 27x = 34x
-48 + 34x + 5x2 = 31 + -27x + -31 + 27x

Reorder the terms:
-48 + 34x + 5x2 = 31 + -31 + -27x + 27x

Combine like terms: 31 + -31 = 0
-48 + 34x + 5x2 = 0 + -27x + 27x
-48 + 34x + 5x2 = -27x + 27x

Combine like terms: -27x + 27x = 0
-48 + 34x + 5x2 = 0

Factor a trinomial.
(-8 + -1x)(6 + -5x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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 = {-8, 1.2}

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