2x^2-31x=-7x^2-5x-16

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Solution for 2x^2-31x=-7x^2-5x-16 equation: 


Simplifying
2x2 + -31x = -7x2 + -5x + -16

Reorder the terms:
-31x + 2x2 = -7x2 + -5x + -16

Reorder the terms:
-31x + 2x2 = -16 + -5x + -7x2

Solving
-31x + 2x2 = -16 + -5x + -7x2

Solving for variable 'x'.

Reorder the terms:
16 + -31x + 5x + 2x2 + 7x2 = -16 + -5x + -7x2 + 16 + 5x + 7x2

Combine like terms: -31x + 5x = -26x
16 + -26x + 2x2 + 7x2 = -16 + -5x + -7x2 + 16 + 5x + 7x2

Combine like terms: 2x2 + 7x2 = 9x2
16 + -26x + 9x2 = -16 + -5x + -7x2 + 16 + 5x + 7x2

Reorder the terms:
16 + -26x + 9x2 = -16 + 16 + -5x + 5x + -7x2 + 7x2

Combine like terms: -16 + 16 = 0
16 + -26x + 9x2 = 0 + -5x + 5x + -7x2 + 7x2
16 + -26x + 9x2 = -5x + 5x + -7x2 + 7x2

Combine like terms: -5x + 5x = 0
16 + -26x + 9x2 = 0 + -7x2 + 7x2
16 + -26x + 9x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
16 + -26x + 9x2 = 0

Factor a trinomial.
(8 + -9x)(2 + -1x) = 0


Subproblem 1
Set the factor '(8 + -9x)' equal to zero and attempt to solve:

Simplifying
8 + -9x = 0

Solving
8 + -9x = 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 + -9x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9x = 0 + -8
-9x = 0 + -8

Combine like terms: 0 + -8 = -8
-9x = -8

Divide each side by '-9'.
x = 0.8888888889

Simplifying
x = 0.8888888889

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.8888888889, 2}

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