e^2-12=-e

Solution for e^2-12=-e equation:

Simplifying
e2 + -12 = -1e

Reorder the terms:
-12 + e2 = -1e

Solving
-12 + e2 = -1e

Solving for variable 'e'.

Reorder the terms:
-12 + e + e2 = -1e + e

Combine like terms: -1e + e = 0
-12 + e + e2 = 0

Factor a trinomial.
(-4 + -1e)(3 + -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 '(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 = {-4, 3}