e^2-5e-84=0

Solution for e^2-5e-84=0 equation:

Simplifying
e2 + -5e + -84 = 0

Reorder the terms:
-84 + -5e + e2 = 0

Solving
-84 + -5e + e2 = 0

Solving for variable 'e'.

Factor a trinomial.
(-7 + -1e)(12 + -1e) = 0

Subproblem 1
Set the factor '(-7 + -1e)' equal to zero and attempt to solve:

Simplifying
-7 + -1e = 0

Solving
-7 + -1e = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1e = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1e = 0 + 7
-1e = 0 + 7

Combine like terms: 0 + 7 = 7
-1e = 7

Divide each side by '-1'.
e = -7

Simplifying
e = -7
Subproblem 2
Set the factor '(12 + -1e)' equal to zero and attempt to solve:

Simplifying
12 + -1e = 0

Solving
12 + -1e = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1e = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1e = 0 + -12
-1e = 0 + -12

Combine like terms: 0 + -12 = -12
-1e = -12

Divide each side by '-1'.
e = 12

Simplifying
e = 12
Solution
e = {-7, 12}