360-x^2-10x=5x+36

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Solution for 360-x^2-10x=5x+36 equation: 


Simplifying
360 + -1x2 + -10x = 5x + 36

Reorder the terms:
360 + -10x + -1x2 = 5x + 36

Reorder the terms:
360 + -10x + -1x2 = 36 + 5x

Solving
360 + -10x + -1x2 = 36 + 5x

Solving for variable 'x'.

Reorder the terms:
360 + -36 + -10x + -5x + -1x2 = 36 + 5x + -36 + -5x

Combine like terms: 360 + -36 = 324
324 + -10x + -5x + -1x2 = 36 + 5x + -36 + -5x

Combine like terms: -10x + -5x = -15x
324 + -15x + -1x2 = 36 + 5x + -36 + -5x

Reorder the terms:
324 + -15x + -1x2 = 36 + -36 + 5x + -5x

Combine like terms: 36 + -36 = 0
324 + -15x + -1x2 = 0 + 5x + -5x
324 + -15x + -1x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
324 + -15x + -1x2 = 0

Factor a trinomial.
(12 + -1x)(27 + x) = 0


Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12

Subproblem 2
Set the factor '(27 + x)' equal to zero and attempt to solve:

Simplifying
27 + x = 0

Solving
27 + x = 0

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

Add '-27' to each side of the equation.
27 + -27 + x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + x = 0 + -27
x = 0 + -27

Combine like terms: 0 + -27 = -27
x = -27

Simplifying
x = -27
Solution
x = {12, -27}

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