8x^2-x^4=12

Solution for 8x^2-x^4=12 equation:

Simplifying
8x2 + -1x4 = 12

Solving
8x2 + -1x4 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 8x2 + -1x4 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 8x2 + -1x4 = 0

Factor a trinomial.
(-6 + x2)(2 + -1x2) = 0

Subproblem 1
Set the factor '(-6 + x2)' equal to zero and attempt to solve:

Simplifying
-6 + x2 = 0

Solving
-6 + x2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x2 = 0 + 6
x2 = 0 + 6

Combine like terms: 0 + 6 = 6
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Subproblem 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 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 + -1x2 = 0 + -2

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

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

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {-2.449489743, 2.449489743, -1.414213562, 1.414213562}