-x^2-2x+100=8x+25

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Solution for -x^2-2x+100=8x+25 equation: 


Simplifying
-1x2 + -2x + 100 = 8x + 25

Reorder the terms:
100 + -2x + -1x2 = 8x + 25

Reorder the terms:
100 + -2x + -1x2 = 25 + 8x

Solving
100 + -2x + -1x2 = 25 + 8x

Solving for variable 'x'.

Reorder the terms:
100 + -25 + -2x + -8x + -1x2 = 25 + 8x + -25 + -8x

Combine like terms: 100 + -25 = 75
75 + -2x + -8x + -1x2 = 25 + 8x + -25 + -8x

Combine like terms: -2x + -8x = -10x
75 + -10x + -1x2 = 25 + 8x + -25 + -8x

Reorder the terms:
75 + -10x + -1x2 = 25 + -25 + 8x + -8x

Combine like terms: 25 + -25 = 0
75 + -10x + -1x2 = 0 + 8x + -8x
75 + -10x + -1x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
75 + -10x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(15 + x) = 0


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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
Solution
x = {5, -15}

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