10z^3-11z^2+3z=0

Solution for 10z^3-11z^2+3z=0 equation:

Simplifying
10z3 + -11z2 + 3z = 0

Reorder the terms:
3z + -11z2 + 10z3 = 0

Solving
3z + -11z2 + 10z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(3 + -11z + 10z2) = 0

Factor a trinomial.
z((1 + -2z)(3 + -5z)) = 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 '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Subproblem 3
Set the factor '(3 + -5z)' equal to zero and attempt to solve:

Simplifying
3 + -5z = 0

Solving
3 + -5z = 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 + -5z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5z = 0 + -3
-5z = 0 + -3

Combine like terms: 0 + -3 = -3
-5z = -3

Divide each side by '-5'.
z = 0.6

Simplifying
z = 0.6
Solution
z = {0, 0.5, 0.6}