e^2=5e+6

Solution for e^2=5e+6 equation:

Simplifying
e2 = 5e + 6

Reorder the terms:
e2 = 6 + 5e

Solving
e2 = 6 + 5e

Solving for variable 'e'.

Reorder the terms:
-6 + -5e + e2 = 6 + 5e + -6 + -5e

Reorder the terms:
-6 + -5e + e2 = 6 + -6 + 5e + -5e

Combine like terms: 6 + -6 = 0
-6 + -5e + e2 = 0 + 5e + -5e
-6 + -5e + e2 = 5e + -5e

Combine like terms: 5e + -5e = 0
-6 + -5e + e2 = 0

Factor a trinomial.
(-1 + -1e)(6 + -1e) = 0

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

Simplifying
-1 + -1e = 0

Solving
-1 + -1e = 0

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

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

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

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

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

Simplifying
e = -1
Subproblem 2
Set the factor '(6 + -1e)' equal to zero and attempt to solve:

Simplifying
6 + -1e = 0

Solving
6 + -1e = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1e = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1e = 0 + -6
-1e = 0 + -6

Combine like terms: 0 + -6 = -6
-1e = -6

Divide each side by '-1'.
e = 6

Simplifying
e = 6
Solution
e = {-1, 6}