3z^4-30z^3+27z^2=

Solution for 3z^4-30z^3+27z^2= equation:

Simplifying
3z4 + -30z3 + 27z2 = 0

Reorder the terms:
27z2 + -30z3 + 3z4 = 0

Solving
27z2 + -30z3 + 3z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z2'.
3z2(9 + -10z + z2) = 0

Factor a trinomial.
3z2((1 + -1z)(9 + -1z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
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
Subproblem 3
Set the factor '(9 + -1z)' equal to zero and attempt to solve:

Simplifying
9 + -1z = 0

Solving
9 + -1z = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1z = 0 + -9
-1z = 0 + -9

Combine like terms: 0 + -9 = -9
-1z = -9

Divide each side by '-1'.
z = 9

Simplifying
z = 9
Solution
z = {0, 1, 9}