3x^2-5x-64=-12+x^2

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Solution for 3x^2-5x-64=-12+x^2 equation: 


Simplifying
3x2 + -5x + -64 = -12 + x2

Reorder the terms:
-64 + -5x + 3x2 = -12 + x2

Solving
-64 + -5x + 3x2 = -12 + x2

Solving for variable 'x'.

Reorder the terms:
-64 + 12 + -5x + 3x2 + -1x2 = -12 + x2 + 12 + -1x2

Combine like terms: -64 + 12 = -52
-52 + -5x + 3x2 + -1x2 = -12 + x2 + 12 + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-52 + -5x + 2x2 = -12 + x2 + 12 + -1x2

Reorder the terms:
-52 + -5x + 2x2 = -12 + 12 + x2 + -1x2

Combine like terms: -12 + 12 = 0
-52 + -5x + 2x2 = 0 + x2 + -1x2
-52 + -5x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-52 + -5x + 2x2 = 0

Factor a trinomial.
(-4 + -1x)(13 + -2x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(13 + -2x)' equal to zero and attempt to solve:

Simplifying
13 + -2x = 0

Solving
13 + -2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2x = 0 + -13
-2x = 0 + -13

Combine like terms: 0 + -13 = -13
-2x = -13

Divide each side by '-2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {-4, 6.5}

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