e^2-e-6=0

Solution for e^2-e-6=0 equation:

Simplifying
e2 + -1e + -6 = 0

Reorder the terms:
-6 + -1e + e2 = 0

Solving
-6 + -1e + e2 = 0

Solving for variable 'e'.

Factor a trinomial.
(-2 + -1e)(3 + -1e) = 0

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

Simplifying
-2 + -1e = 0

Solving
-2 + -1e = 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 + -1e = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1e = 0 + 2
-1e = 0 + 2

Combine like terms: 0 + 2 = 2
-1e = 2

Divide each side by '-1'.
e = -2

Simplifying
e = -2
Subproblem 2
Set the factor '(3 + -1e)' equal to zero and attempt to solve:

Simplifying
3 + -1e = 0

Solving
3 + -1e = 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 + -1e = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1e = 0 + -3
-1e = 0 + -3

Combine like terms: 0 + -3 = -3
-1e = -3

Divide each side by '-1'.
e = 3

Simplifying
e = 3
Solution
e = {-2, 3}