2x^4-76x^2=-144

Solution for 2x^4-76x^2=-144 equation:

Simplifying
2x4 + -76x2 = -144

Reorder the terms:
-76x2 + 2x4 = -144

Solving
-76x2 + 2x4 = -144

Solving for variable 'x'.

Reorder the terms:
144 + -76x2 + 2x4 = -144 + 144

Combine like terms: -144 + 144 = 0
144 + -76x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(72 + -38x2 + x4) = 0

Factor a trinomial.
2((2 + -1x2)(36 + -1x2)) = 0

Factor a difference between two squares.
2((2 + -1x2)((6 + x)(6 + -1x))) = 0

Ignore the factor 2.
Subproblem 1
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}
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

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

Simplifying
x = 6
Solution
x = {-1.414213562, 1.414213562, -6, 6}