3e^2+19e+20=0

Solution for 3e^2+19e+20=0 equation:

Simplifying
3e2 + 19e + 20 = 0

Reorder the terms:
20 + 19e + 3e2 = 0

Solving
20 + 19e + 3e2 = 0

Solving for variable 'e'.

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

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

Simplifying
5 + e = 0

Solving
5 + e = 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 + e = 0 + -5

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

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

Simplifying
e = -5
Subproblem 2
Set the factor '(4 + 3e)' equal to zero and attempt to solve:

Simplifying
4 + 3e = 0

Solving
4 + 3e = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3e = 0 + -4

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

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

Divide each side by '3'.
e = -1.333333333

Simplifying
e = -1.333333333
Solution
e = {-5, -1.333333333}