e^2-3e=10

Solution for e^2-3e=10 equation:

Simplifying
e2 + -3e = 10

Reorder the terms:
-3e + e2 = 10

Solving
-3e + e2 = 10

Solving for variable 'e'.

Reorder the terms:
-10 + -3e + e2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -3e + e2 = 0

Factor a trinomial.
(-2 + -1e)(5 + -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 '(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 = {-2, 5}