6z^3=5z^2+6z

Solution for 6z^3=5z^2+6z equation:

Simplifying
6z3 = 5z2 + 6z

Reorder the terms:
6z3 = 6z + 5z2

Solving
6z3 = 6z + 5z2

Solving for variable 'z'.

Reorder the terms:
-6z + -5z2 + 6z3 = 6z + 5z2 + -6z + -5z2

Reorder the terms:
-6z + -5z2 + 6z3 = 6z + -6z + 5z2 + -5z2

Combine like terms: 6z + -6z = 0
-6z + -5z2 + 6z3 = 0 + 5z2 + -5z2
-6z + -5z2 + 6z3 = 5z2 + -5z2

Combine like terms: 5z2 + -5z2 = 0
-6z + -5z2 + 6z3 = 0

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

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

Simplifying
-2 + -3z = 0

Solving
-2 + -3z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3z = 0 + 2
-3z = 0 + 2

Combine like terms: 0 + 2 = 2
-3z = 2

Divide each side by '-3'.
z = -0.6666666667

Simplifying
z = -0.6666666667
Subproblem 3
Set the factor '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 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 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {0, -0.6666666667, 1.5}