6e^3-5e^2-6e=0

Solution for 6e^3-5e^2-6e=0 equation:

Simplifying
6e3 + -5e2 + -6e = 0

Reorder the terms:
-6e + -5e2 + 6e3 = 0

Solving
-6e + -5e2 + 6e3 = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), 'e'.
e(-6 + -5e + 6e2) = 0

Factor a trinomial.
e((-2 + -3e)(3 + -2e)) = 0

Subproblem 1
Set the factor 'e' equal to zero and attempt to solve:

Simplifying
e = 0

Solving
e = 0

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

Simplifying
e = 0
Subproblem 2
Set the factor '(-2 + -3e)' equal to zero and attempt to solve:

Simplifying
-2 + -3e = 0

Solving
-2 + -3e = 0

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

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

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

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

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

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

Simplifying
3 + -2e = 0

Solving
3 + -2e = 0

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

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

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

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

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

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