12e^2-8e-15=0

Solution for 12e^2-8e-15=0 equation:

Simplifying
12e2 + -8e + -15 = 0

Reorder the terms:
-15 + -8e + 12e2 = 0

Solving
-15 + -8e + 12e2 = 0

Solving for variable 'e'.

Factor a trinomial.
(-5 + -6e)(3 + -2e) = 0

Subproblem 1
Set the factor '(-5 + -6e)' equal to zero and attempt to solve:

Simplifying
-5 + -6e = 0

Solving
-5 + -6e = 0

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

Add '5' to each side of the equation.
-5 + 5 + -6e = 0 + 5

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

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

Divide each side by '-6'.
e = -0.8333333333

Simplifying
e = -0.8333333333
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 = {-0.8333333333, 1.5}