180=x^2+(100-2x)

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Solution for 180=x^2+(100-2x) equation: 


Simplifying
180 = x2 + (100 + -2x)

Remove parenthesis around (100 + -2x)
180 = x2 + 100 + -2x

Reorder the terms:
180 = 100 + -2x + x2

Solving
180 = 100 + -2x + x2

Solving for variable 'x'.

Combine like terms: 180 + -100 = 80
80 + 2x + -1x2 = 100 + -2x + x2 + -100 + 2x + -1x2

Reorder the terms:
80 + 2x + -1x2 = 100 + -100 + -2x + 2x + x2 + -1x2

Combine like terms: 100 + -100 = 0
80 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2
80 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
80 + 2x + -1x2 = 0 + x2 + -1x2
80 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
80 + 2x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(8 + x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

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 = {10, -8}

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