-2z(4z^2-3z+1)-z(3z^2+2z-1)=0

Solution for -2z(4z^2-3z+1)-z(3z^2+2z-1)=0 equation:

Simplifying
-2z(4z2 + -3z + 1) + -1z(3z2 + 2z + -1) = 0

Reorder the terms:
-2z(1 + -3z + 4z2) + -1z(3z2 + 2z + -1) = 0
(1 * -2z + -3z * -2z + 4z2 * -2z) + -1z(3z2 + 2z + -1) = 0
(-2z + 6z2 + -8z3) + -1z(3z2 + 2z + -1) = 0

Reorder the terms:
-2z + 6z2 + -8z3 + -1z(-1 + 2z + 3z2) = 0
-2z + 6z2 + -8z3 + (-1 * -1z + 2z * -1z + 3z2 * -1z) = 0
-2z + 6z2 + -8z3 + (1z + -2z2 + -3z3) = 0

Reorder the terms:
-2z + 1z + 6z2 + -2z2 + -8z3 + -3z3 = 0

Combine like terms: -2z + 1z = -1z
-1z + 6z2 + -2z2 + -8z3 + -3z3 = 0

Combine like terms: 6z2 + -2z2 = 4z2
-1z + 4z2 + -8z3 + -3z3 = 0

Combine like terms: -8z3 + -3z3 = -11z3
-1z + 4z2 + -11z3 = 0

Solving
-1z + 4z2 + -11z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-1 + 4z + -11z2) = 0

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(-1 + 4z + -11z2)' equal to zero and attempt to solve:

Simplifying
-1 + 4z + -11z2 = 0

Solving
-1 + 4z + -11z2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
0.09090909091 + -0.3636363636z + z2 = 0

Move the constant term to the right:

Add '-0.09090909091' to each side of the equation.
0.09090909091 + -0.3636363636z + -0.09090909091 + z2 = 0 + -0.09090909091

Reorder the terms:
0.09090909091 + -0.09090909091 + -0.3636363636z + z2 = 0 + -0.09090909091

Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000
0.00000000000 + -0.3636363636z + z2 = 0 + -0.09090909091
-0.3636363636z + z2 = 0 + -0.09090909091

Combine like terms: 0 + -0.09090909091 = -0.09090909091
-0.3636363636z + z2 = -0.09090909091

The z term is -0.3636363636z.  Take half its coefficient (-0.1818181818).
Square it (0.03305785123) and add it to both sides.

Add '0.03305785123' to each side of the equation.
-0.3636363636z + 0.03305785123 + z2 = -0.09090909091 + 0.03305785123

Reorder the terms:
0.03305785123 + -0.3636363636z + z2 = -0.09090909091 + 0.03305785123

Combine like terms: -0.09090909091 + 0.03305785123 = -0.05785123968
0.03305785123 + -0.3636363636z + z2 = -0.05785123968

Factor a perfect square on the left side:
(z + -0.1818181818)(z + -0.1818181818) = -0.05785123968

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}