6e^2=5e+6

Solution for 6e^2=5e+6 equation:

Simplifying
6e2 = 5e + 6

Reorder the terms:
6e2 = 6 + 5e

Solving
6e2 = 6 + 5e

Solving for variable 'e'.

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

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

Combine like terms: 6 + -6 = 0
-6 + -5e + 6e2 = 0 + 5e + -5e
-6 + -5e + 6e2 = 5e + -5e

Combine like terms: 5e + -5e = 0
-6 + -5e + 6e2 = 0

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

Subproblem 1
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 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
Solution
e = {-0.6666666667, 1.5}