(z^4+2z^2)-(3z^4+z^3+3z^2)=0

Solution for (z^4+2z^2)-(3z^4+z^3+3z^2)=0 equation:

Simplifying
(z4 + 2z2) + -1(3z4 + z3 + 3z2) = 0

Reorder the terms:
(2z2 + z4) + -1(3z4 + z3 + 3z2) = 0

Remove parenthesis around (2z2 + z4)
2z2 + z4 + -1(3z4 + z3 + 3z2) = 0

Reorder the terms:
2z2 + z4 + -1(3z2 + z3 + 3z4) = 0
2z2 + z4 + (3z2 * -1 + z3 * -1 + 3z4 * -1) = 0
2z2 + z4 + (-3z2 + -1z3 + -3z4) = 0

Reorder the terms:
2z2 + -3z2 + -1z3 + z4 + -3z4 = 0

Combine like terms: 2z2 + -3z2 = -1z2
-1z2 + -1z3 + z4 + -3z4 = 0

Combine like terms: z4 + -3z4 = -2z4
-1z2 + -1z3 + -2z4 = 0

Solving
-1z2 + -1z3 + -2z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '-1z2'.
-1z2(1 + z + 2z2) = 0

Ignore the factor -1.
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 '(1 + z + 2z2)' equal to zero and attempt to solve:

Simplifying
1 + z + 2z2 = 0

Solving
1 + z + 2z2 = 0

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

Divide each side by '2'.
0.5 + 0.5z + z2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.5z + -0.5 + z2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.5z + z2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.5z + z2 = 0 + -0.5
0.5z + z2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.5z + z2 = -0.5

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5z + 0.25 + z2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.5z + z2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.5z + z2 = -0.25

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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