z^5-28z^3+27z=0

Solution for z^5-28z^3+27z=0 equation:

Simplifying
z5 + -28z3 + 27z = 0

Reorder the terms:
27z + -28z3 + z5 = 0

Solving
27z + -28z3 + z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(27 + -28z2 + z4) = 0

Factor a trinomial.
z((1 + -1z2)(27 + -1z2)) = 0

Factor a difference between two squares.
z(((1 + z)(1 + -1z))(27 + -1z2)) = 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 '(27 + -1z2)' equal to zero and attempt to solve:

Simplifying
27 + -1z2 = 0

Solving
27 + -1z2 = 0

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

Add '-27' to each side of the equation.
27 + -27 + -1z2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -1z2 = 0 + -27
-1z2 = 0 + -27

Combine like terms: 0 + -27 = -27
-1z2 = -27

Divide each side by '-1'.
z2 = 27

Simplifying
z2 = 27

Take the square root of each side:
z = {-5.196152423, 5.196152423}
Subproblem 3
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 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 + z = 0 + -1

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

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 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 + -1z = 0 + -1

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

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

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {0, -5.196152423, 5.196152423, -1, 1}