0=60x^4-15x^2

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Solution for 0=60x^4-15x^2 equation: 


Simplifying
0 = 60x4 + -15x2

Reorder the terms:
0 = -15x2 + 60x4

Solving
0 = -15x2 + 60x4

Solving for variable 'x'.
Remove the zero:
15x2 + -60x4 = -15x2 + 60x4 + 15x2 + -60x4

Reorder the terms:
15x2 + -60x4 = -15x2 + 15x2 + 60x4 + -60x4

Combine like terms: -15x2 + 15x2 = 0
15x2 + -60x4 = 0 + 60x4 + -60x4
15x2 + -60x4 = 60x4 + -60x4

Combine like terms: 60x4 + -60x4 = 0
15x2 + -60x4 = 0

Factor out the Greatest Common Factor (GCF), '15x2'.
15x2(1 + -4x2) = 0

Factor a difference between two squares.
15x2((1 + 2x)(1 + -2x)) = 0

Ignore the factor 15.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

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

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -0.5, 0.5}

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