18z^3-15z^2+12z=0

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Solution for 18z^3-15z^2+12z=0 equation: 


Simplifying
18z3 + -15z2 + 12z = 0

Reorder the terms:
12z + -15z2 + 18z3 = 0

Solving
12z + -15z2 + 18z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(4 + -5z + 6z2) = 0

Ignore the factor 3.

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 '(4 + -5z + 6z2)' equal to zero and attempt to solve:

Simplifying
4 + -5z + 6z2 = 0

Solving
4 + -5z + 6z2 = 0

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

Divide each side by '6'.
0.6666666667 + -0.8333333333z + z2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -0.8333333333z + -0.6666666667 + z2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -0.8333333333z + z2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -0.8333333333z + z2 = 0 + -0.6666666667
-0.8333333333z + z2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-0.8333333333z + z2 = -0.6666666667

The z term is -0.8333333333z.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333z + 0.1736111111 + z2 = -0.6666666667 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333z + z2 = -0.6666666667 + 0.1736111111

Combine like terms: -0.6666666667 + 0.1736111111 = -0.4930555556
0.1736111111 + -0.8333333333z + z2 = -0.4930555556

Factor a perfect square on the left side:
(z + -0.4166666667)(z + -0.4166666667) = -0.4930555556

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}

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