5E^2+6E=6E^3

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

Simplifying
5E2 + 6E = 6E3

Reorder the terms:
6E + 5E2 = 6E3

Solving
6E + 5E2 = 6E3

Solving for variable 'E'.

Combine like terms: 6E3 + -6E3 = 0
6E + 5E2 + -6E3 = 0

Factor out the Greatest Common Factor (GCF), 'E'.
E(6 + 5E + -6E2) = 0

Factor a trinomial.
E((3 + -2E)(2 + 3E)) = 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 '(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
Subproblem 3
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
Solution
E = {0, 1.5, -0.6666666667}