6z^4-13z^2+6=0

Solution for 6z^4-13z^2+6=0 equation:

Simplifying
6z4 + -13z2 + 6 = 0

Reorder the terms:
6 + -13z2 + 6z4 = 0

Solving
6 + -13z2 + 6z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -3z2)(3 + -2z2) = 0

Subproblem 1
Set the factor '(2 + -3z2)' equal to zero and attempt to solve:

Simplifying
2 + -3z2 = 0

Solving
2 + -3z2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3z2 = 0 + -2
-3z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3z2 = -2

Divide each side by '-3'.
z2 = 0.6666666667

Simplifying
z2 = 0.6666666667

Take the square root of each side:
z = {-0.816496581, 0.816496581}
Subproblem 2
Set the factor '(3 + -2z2)' equal to zero and attempt to solve:

Simplifying
3 + -2z2 = 0

Solving
3 + -2z2 = 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 + -2z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z2 = 0 + -3
-2z2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2z2 = -3

Divide each side by '-2'.
z2 = 1.5

Simplifying
z2 = 1.5

Take the square root of each side:
z = {-1.224744871, 1.224744871}
Solution
z = {-0.816496581, 0.816496581, -1.224744871, 1.224744871}