9z^3+27z^2=162z

Solution for 9z^3+27z^2=162z equation:

Simplifying
9z3 + 27z2 = 162z

Reorder the terms:
27z2 + 9z3 = 162z

Solving
27z2 + 9z3 = 162z

Solving for variable 'z'.

Reorder the terms:
-162z + 27z2 + 9z3 = 162z + -162z

Combine like terms: 162z + -162z = 0
-162z + 27z2 + 9z3 = 0

Factor out the Greatest Common Factor (GCF), '9z'.
9z(-18 + 3z + z2) = 0

Factor a trinomial.
9z((-6 + -1z)(3 + -1z)) = 0

Ignore the factor 9.
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 '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
Subproblem 3
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {0, -6, 3}