6z^4-7z^2+2=0

Solution for 6z^4-7z^2+2=0 equation:

Simplifying
6z4 + -7z2 + 2 = 0

Reorder the terms:
2 + -7z2 + 6z4 = 0

Solving
2 + -7z2 + 6z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -2z2)(2 + -3z2) = 0

Subproblem 1
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

Take the square root of each side:
z = {-0.707106781, 0.707106781}
Subproblem 2
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}
Solution
z = {-0.707106781, 0.707106781, -0.816496581, 0.816496581}