12X^2=X^4+36

Solution for 12X^2=X^4+36 equation:

Simplifying
12X2 = X4 + 36

Reorder the terms:
12X2 = 36 + X4

Solving
12X2 = 36 + X4

Solving for variable 'X'.

Reorder the terms:
-36 + 12X2 + -1X4 = 36 + X4 + -36 + -1X4

Reorder the terms:
-36 + 12X2 + -1X4 = 36 + -36 + X4 + -1X4

Combine like terms: 36 + -36 = 0
-36 + 12X2 + -1X4 = 0 + X4 + -1X4
-36 + 12X2 + -1X4 = X4 + -1X4

Combine like terms: X4 + -1X4 = 0
-36 + 12X2 + -1X4 = 0

Factor a trinomial.
(-6 + X2)(6 + -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 '(6 + -1X2)' equal to zero and attempt to solve:

Simplifying
6 + -1X2 = 0

Solving
6 + -1X2 = 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 + -1X2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1X2 = 0 + -6
-1X2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1X2 = -6

Divide each side by '-1'.
X2 = 6

Simplifying
X2 = 6

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