6e^2+5e-6=0

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

Simplifying
6e2 + 5e + -6 = 0

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

Solving
-6 + 5e + 6e2 = 0

Solving for variable 'e'.

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

Subproblem 1
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 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
Solution
e = {-1.5, 0.6666666667}