-12z^5+12z^4+10z^3=

Solution for -12z^5+12z^4+10z^3= equation:

Simplifying
-12z5 + 12z4 + 10z3 = 0

Reorder the terms:
10z3 + 12z4 + -12z5 = 0

Solving
10z3 + 12z4 + -12z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2z3'.
2z3(5 + 6z + -6z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'z3' equal to zero and attempt to solve:

Simplifying
z3 = 0

Solving
z3 = 0

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

Simplifying
z3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(5 + 6z + -6z2)' equal to zero and attempt to solve:

Simplifying
5 + 6z + -6z2 = 0

Solving
5 + 6z + -6z2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.8333333333 + -1z + z2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -1z + 0.8333333333 + z2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -1z + z2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -1z + z2 = 0 + 0.8333333333
-1z + z2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-1z + z2 = 0.8333333333

The z term is -1z.  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.
-1z + 0.25 + z2 = 0.8333333333 + 0.25

Reorder the terms:
0.25 + -1z + z2 = 0.8333333333 + 0.25

Combine like terms: 0.8333333333 + 0.25 = 1.0833333333
0.25 + -1z + z2 = 1.0833333333

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = 1.0833333333

Calculate the square root of the right side: 1.040833

Break this problem into two subproblems by setting 
(z + -0.5) equal to 1.040833 and -1.040833.

Subproblem 1
z + -0.5 = 1.040833

Simplifying
z + -0.5 = 1.040833

Reorder the terms:
-0.5 + z = 1.040833

Solving
-0.5 + z = 1.040833

Solving for variable 'z'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + z = 1.040833 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + z = 1.040833 + 0.5
z = 1.040833 + 0.5

Combine like terms: 1.040833 + 0.5 = 1.540833
z = 1.540833

Simplifying
z = 1.540833

Subproblem 2
z + -0.5 = -1.040833

Simplifying
z + -0.5 = -1.040833

Reorder the terms:
-0.5 + z = -1.040833

Solving
-0.5 + z = -1.040833

Solving for variable 'z'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + z = -1.040833 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + z = -1.040833 + 0.5
z = -1.040833 + 0.5

Combine like terms: -1.040833 + 0.5 = -0.540833
z = -0.540833

Simplifying
z = -0.540833

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.540833, -0.540833}
Solution
z = {1.540833, -0.540833}