x^2=-2x^2+96x-765

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Solution for x^2=-2x^2+96x-765 equation: 


Simplifying
x2 = -2x2 + 96x + -765

Reorder the terms:
x2 = -765 + 96x + -2x2

Solving
x2 = -765 + 96x + -2x2

Solving for variable 'x'.

Reorder the terms:
765 + -96x + x2 + 2x2 = -765 + 96x + -2x2 + 765 + -96x + 2x2

Combine like terms: x2 + 2x2 = 3x2
765 + -96x + 3x2 = -765 + 96x + -2x2 + 765 + -96x + 2x2

Reorder the terms:
765 + -96x + 3x2 = -765 + 765 + 96x + -96x + -2x2 + 2x2

Combine like terms: -765 + 765 = 0
765 + -96x + 3x2 = 0 + 96x + -96x + -2x2 + 2x2
765 + -96x + 3x2 = 96x + -96x + -2x2 + 2x2

Combine like terms: 96x + -96x = 0
765 + -96x + 3x2 = 0 + -2x2 + 2x2
765 + -96x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
765 + -96x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(255 + -32x + x2) = 0

Factor a trinomial.
3((15 + -1x)(17 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 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 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15

Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {15, 17}

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