-2x^2-31x-14=-6+8x-7x^2

Solution for -2x^2-31x-14=-6+8x-7x^2 equation:

Simplifying
-2x2 + -31x + -14 = -6 + 8x + -7x2

Reorder the terms:
-14 + -31x + -2x2 = -6 + 8x + -7x2

Solving
-14 + -31x + -2x2 = -6 + 8x + -7x2

Solving for variable 'x'.

Reorder the terms:
-14 + 6 + -31x + -8x + -2x2 + 7x2 = -6 + 8x + -7x2 + 6 + -8x + 7x2

Combine like terms: -14 + 6 = -8
-8 + -31x + -8x + -2x2 + 7x2 = -6 + 8x + -7x2 + 6 + -8x + 7x2

Combine like terms: -31x + -8x = -39x
-8 + -39x + -2x2 + 7x2 = -6 + 8x + -7x2 + 6 + -8x + 7x2

Combine like terms: -2x2 + 7x2 = 5x2
-8 + -39x + 5x2 = -6 + 8x + -7x2 + 6 + -8x + 7x2

Reorder the terms:
-8 + -39x + 5x2 = -6 + 6 + 8x + -8x + -7x2 + 7x2

Combine like terms: -6 + 6 = 0
-8 + -39x + 5x2 = 0 + 8x + -8x + -7x2 + 7x2
-8 + -39x + 5x2 = 8x + -8x + -7x2 + 7x2

Combine like terms: 8x + -8x = 0
-8 + -39x + 5x2 = 0 + -7x2 + 7x2
-8 + -39x + 5x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-8 + -39x + 5x2 = 0

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

Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2
Subproblem 2
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
Solution
x = {-0.2, 8}