12x^2-64=-x^4

Solution for 12x^2-64=-x^4 equation:

Simplifying
12x2 + -64 = -1x4

Reorder the terms:
-64 + 12x2 = -1x4

Solving
-64 + 12x2 = -1x4

Solving for variable 'x'.

Combine like terms: -1x4 + x4 = 0
-64 + 12x2 + x4 = 0

Factor a trinomial.
(-16 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
(-16 + -1x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(-16 + -1x2)' equal to zero and attempt to solve:

Simplifying
-16 + -1x2 = 0

Solving
-16 + -1x2 = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x2 = 0 + 16
-1x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-1x2 = 16

Divide each side by '-1'.
x2 = -16

Simplifying
x2 = -16

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2, 2}