3e^2-8e=80

Solution for 3e^2-8e=80 equation:

Simplifying
3e2 + -8e = 80

Reorder the terms:
-8e + 3e2 = 80

Solving
-8e + 3e2 = 80

Solving for variable 'e'.

Reorder the terms:
-80 + -8e + 3e2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + -8e + 3e2 = 0

Factor a trinomial.
(-4 + -1e)(20 + -3e) = 0

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

Simplifying
-4 + -1e = 0

Solving
-4 + -1e = 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 + -1e = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1e = 0 + 4
-1e = 0 + 4

Combine like terms: 0 + 4 = 4
-1e = 4

Divide each side by '-1'.
e = -4

Simplifying
e = -4
Subproblem 2
Set the factor '(20 + -3e)' equal to zero and attempt to solve:

Simplifying
20 + -3e = 0

Solving
20 + -3e = 0

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

Add '-20' to each side of the equation.
20 + -20 + -3e = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -3e = 0 + -20
-3e = 0 + -20

Combine like terms: 0 + -20 = -20
-3e = -20

Divide each side by '-3'.
e = 6.666666667

Simplifying
e = 6.666666667
Solution
e = {-4, 6.666666667}