12e^2+17e+6=

Solution for 12e^2+17e+6= equation:

Simplifying
12e2 + 17e + 6 = 0

Reorder the terms:
6 + 17e + 12e2 = 0

Solving
6 + 17e + 12e2 = 0

Solving for variable 'e'.

Factor a trinomial.
(3 + 4e)(2 + 3e) = 0

Subproblem 1
Set the factor '(3 + 4e)' equal to zero and attempt to solve:

Simplifying
3 + 4e = 0

Solving
3 + 4e = 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 + 4e = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4e = 0 + -3
4e = 0 + -3

Combine like terms: 0 + -3 = -3
4e = -3

Divide each side by '4'.
e = -0.75

Simplifying
e = -0.75
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 = {-0.75, -0.6666666667}