2x*x-8=31x-2x*x

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Solution for 2x*x-8=31x-2x*x equation:


Simplifying
2x * x + -8 = 31x + -2x * x

Multiply x * x
2x2 + -8 = 31x + -2x * x

Reorder the terms:
-8 + 2x2 = 31x + -2x * x

Multiply x * x
-8 + 2x2 = 31x + -2x2

Solving
-8 + 2x2 = 31x + -2x2

Solving for variable 'x'.

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

Combine like terms: 2x2 + 2x2 = 4x2
-8 + -31x + 4x2 = 31x + -2x2 + -31x + 2x2

Reorder the terms:
-8 + -31x + 4x2 = 31x + -31x + -2x2 + 2x2

Combine like terms: 31x + -31x = 0
-8 + -31x + 4x2 = 0 + -2x2 + 2x2
-8 + -31x + 4x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-8 + -31x + 4x2 = 0

Factor a trinomial.
(-1 + -4x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

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 = {-0.25, 8}

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