32z^6+40z^4+12z^2=

Solution for 32z^6+40z^4+12z^2= equation:

Simplifying
32z6 + 40z4 + 12z2 = 0

Reorder the terms:
12z2 + 40z4 + 32z6 = 0

Solving
12z2 + 40z4 + 32z6 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z2'.
4z2(3 + 10z2 + 8z4) = 0

Factor a trinomial.
4z2((3 + 4z2)(1 + 2z2)) = 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 '(3 + 4z2)' equal to zero and attempt to solve:

Simplifying
3 + 4z2 = 0

Solving
3 + 4z2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4z2 = 0 + -3
4z2 = 0 + -3

Combine like terms: 0 + -3 = -3
4z2 = -3

Divide each side by '4'.
z2 = -0.75

Simplifying
z2 = -0.75

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + 2z2)' equal to zero and attempt to solve:

Simplifying
1 + 2z2 = 0

Solving
1 + 2z2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2z2 = 0 + -1
2z2 = 0 + -1

Combine like terms: 0 + -1 = -1
2z2 = -1

Divide each side by '2'.
z2 = -0.5

Simplifying
z2 = -0.5

The solution to this equation could not be determined.

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