60z^6-118z^5=56z^4

Solution for 60z^6-118z^5=56z^4 equation:

Simplifying
60z6 + -118z5 = 56z4

Reorder the terms:
-118z5 + 60z6 = 56z4

Solving
-118z5 + 60z6 = 56z4

Solving for variable 'z'.

Reorder the terms:
-56z4 + -118z5 + 60z6 = 56z4 + -56z4

Combine like terms: 56z4 + -56z4 = 0
-56z4 + -118z5 + 60z6 = 0

Factor out the Greatest Common Factor (GCF), '2z4'.
2z4(-28 + -59z + 30z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'z4' equal to zero and attempt to solve:

Simplifying
z4 = 0

Solving
z4 = 0

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

Simplifying
z4 = 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 '(-28 + -59z + 30z2)' equal to zero and attempt to solve:

Simplifying
-28 + -59z + 30z2 = 0

Solving
-28 + -59z + 30z2 = 0

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

Divide each side by '30'.
-0.9333333333 + -1.966666667z + z2 = 0.0

Move the constant term to the right:

Add '0.9333333333' to each side of the equation.
-0.9333333333 + -1.966666667z + 0.9333333333 + z2 = 0.0 + 0.9333333333

Reorder the terms:
-0.9333333333 + 0.9333333333 + -1.966666667z + z2 = 0.0 + 0.9333333333

Combine like terms: -0.9333333333 + 0.9333333333 = 0.0000000000
0.0000000000 + -1.966666667z + z2 = 0.0 + 0.9333333333
-1.966666667z + z2 = 0.0 + 0.9333333333

Combine like terms: 0.0 + 0.9333333333 = 0.9333333333
-1.966666667z + z2 = 0.9333333333

The z term is -1.966666667z.  Take half its coefficient (-0.9833333335).
Square it (0.9669444448) and add it to both sides.

Add '0.9669444448' to each side of the equation.
-1.966666667z + 0.9669444448 + z2 = 0.9333333333 + 0.9669444448

Reorder the terms:
0.9669444448 + -1.966666667z + z2 = 0.9333333333 + 0.9669444448

Combine like terms: 0.9333333333 + 0.9669444448 = 1.9002777781
0.9669444448 + -1.966666667z + z2 = 1.9002777781

Factor a perfect square on the left side:
(z + -0.9833333335)(z + -0.9833333335) = 1.9002777781

Calculate the square root of the right side: 1.378505632

Break this problem into two subproblems by setting 
(z + -0.9833333335) equal to 1.378505632 and -1.378505632.

Subproblem 1
z + -0.9833333335 = 1.378505632

Simplifying
z + -0.9833333335 = 1.378505632

Reorder the terms:
-0.9833333335 + z = 1.378505632

Solving
-0.9833333335 + z = 1.378505632

Solving for variable 'z'.

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

Add '0.9833333335' to each side of the equation.
-0.9833333335 + 0.9833333335 + z = 1.378505632 + 0.9833333335

Combine like terms: -0.9833333335 + 0.9833333335 = 0.0000000000
0.0000000000 + z = 1.378505632 + 0.9833333335
z = 1.378505632 + 0.9833333335

Combine like terms: 1.378505632 + 0.9833333335 = 2.3618389655
z = 2.3618389655

Simplifying
z = 2.3618389655

Subproblem 2
z + -0.9833333335 = -1.378505632

Simplifying
z + -0.9833333335 = -1.378505632

Reorder the terms:
-0.9833333335 + z = -1.378505632

Solving
-0.9833333335 + z = -1.378505632

Solving for variable 'z'.

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

Add '0.9833333335' to each side of the equation.
-0.9833333335 + 0.9833333335 + z = -1.378505632 + 0.9833333335

Combine like terms: -0.9833333335 + 0.9833333335 = 0.0000000000
0.0000000000 + z = -1.378505632 + 0.9833333335
z = -1.378505632 + 0.9833333335

Combine like terms: -1.378505632 + 0.9833333335 = -0.3951722985
z = -0.3951722985

Simplifying
z = -0.3951722985

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {2.3618389655, -0.3951722985}
Solution
z = {2.3618389655, -0.3951722985}