5x^2-6x=6x^2-16

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Solution for 5x^2-6x=6x^2-16 equation: 


Simplifying
5x2 + -6x = 6x2 + -16

Reorder the terms:
-6x + 5x2 = 6x2 + -16

Reorder the terms:
-6x + 5x2 = -16 + 6x2

Solving
-6x + 5x2 = -16 + 6x2

Solving for variable 'x'.

Reorder the terms:
16 + -6x + 5x2 + -6x2 = -16 + 6x2 + 16 + -6x2

Combine like terms: 5x2 + -6x2 = -1x2
16 + -6x + -1x2 = -16 + 6x2 + 16 + -6x2

Reorder the terms:
16 + -6x + -1x2 = -16 + 16 + 6x2 + -6x2

Combine like terms: -16 + 16 = 0
16 + -6x + -1x2 = 0 + 6x2 + -6x2
16 + -6x + -1x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
16 + -6x + -1x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

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

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

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

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

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