36z^6+8z^4-60z^2=0

Solution for 36z^6+8z^4-60z^2=0 equation:

Simplifying
36z6 + 8z4 + -60z2 = 0

Reorder the terms:
-60z2 + 8z4 + 36z6 = 0

Solving
-60z2 + 8z4 + 36z6 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z2'.
4z2(-15 + 2z2 + 9z4) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(-15 + 2z2 + 9z4)' equal to zero and attempt to solve:

Simplifying
-15 + 2z2 + 9z4 = 0

Solving
-15 + 2z2 + 9z4 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-1.666666667 + 0.2222222222z2 + z4 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 0.2222222222z2 + 1.666666667 + z4 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 0.2222222222z2 + z4 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 0.2222222222z2 + z4 = 0 + 1.666666667
0.2222222222z2 + z4 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
0.2222222222z2 + z4 = 1.666666667

The z term is 0.2222222222z2.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222z2 + 0.01234567901 + z4 = 1.666666667 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222z2 + z4 = 1.666666667 + 0.01234567901

Combine like terms: 1.666666667 + 0.01234567901 = 1.67901234601
0.01234567901 + 0.2222222222z2 + z4 = 1.67901234601

Factor a perfect square on the left side:
(z2 + 0.1111111111)(z2 + 0.1111111111) = 1.67901234601

Calculate the square root of the right side: 1.295767088

Break this problem into two subproblems by setting 
(z2 + 0.1111111111) equal to 1.295767088 and -1.295767088.

Subproblem 1
z2 + 0.1111111111 = 1.295767088

Simplifying
z2 + 0.1111111111 = 1.295767088

Reorder the terms:
0.1111111111 + z2 = 1.295767088

Solving
0.1111111111 + z2 = 1.295767088

Solving for variable 'z'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + z2 = 1.295767088 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + z2 = 1.295767088 + -0.1111111111
z2 = 1.295767088 + -0.1111111111

Combine like terms: 1.295767088 + -0.1111111111 = 1.1846559769
z2 = 1.1846559769

Simplifying
z2 = 1.1846559769

Take the square root of each side:
z = {-1.088419026, 1.088419026}

Subproblem 2
z2 + 0.1111111111 = -1.295767088

Simplifying
z2 + 0.1111111111 = -1.295767088

Reorder the terms:
0.1111111111 + z2 = -1.295767088

Solving
0.1111111111 + z2 = -1.295767088

Solving for variable 'z'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + z2 = -1.295767088 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + z2 = -1.295767088 + -0.1111111111
z2 = -1.295767088 + -0.1111111111

Combine like terms: -1.295767088 + -0.1111111111 = -1.4068781991
z2 = -1.4068781991

Simplifying
z2 = -1.4068781991

Reorder the terms:
1.4068781991 + z2 = -1.4068781991 + 1.4068781991

Combine like terms: -1.4068781991 + 1.4068781991 = 0.0000000000
1.4068781991 + z2 = 0.0000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}