2e^2+7e+6=0

Solution for 2e^2+7e+6=0 equation:

Simplifying
2e2 + 7e + 6 = 0

Reorder the terms:
6 + 7e + 2e2 = 0

Solving
6 + 7e + 2e2 = 0

Solving for variable 'e'.

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

Subproblem 1
Set the factor '(2 + e)' equal to zero and attempt to solve:

Simplifying
2 + e = 0

Solving
2 + e = 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 + e = 0 + -2

Combine like terms: 2 + -2 = 0
0 + e = 0 + -2
e = 0 + -2

Combine like terms: 0 + -2 = -2
e = -2

Simplifying
e = -2
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 = {-2, -1.5}