e^2-e-20=0

Solution for e^2-e-20=0 equation:

Simplifying
e2 + -1e + -20 = 0

Reorder the terms:
-20 + -1e + e2 = 0

Solving
-20 + -1e + e2 = 0

Solving for variable 'e'.

Factor a trinomial.
(-4 + -1e)(5 + -1e) = 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 '(5 + -1e)' equal to zero and attempt to solve:

Simplifying
5 + -1e = 0

Solving
5 + -1e = 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 + -1e = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1e = 0 + -5
-1e = 0 + -5

Combine like terms: 0 + -5 = -5
-1e = -5

Divide each side by '-1'.
e = 5

Simplifying
e = 5
Solution
e = {-4, 5}