n^2+10n=2n-15

Solution for n^2+10n=2n-15 equation:

Simplifying
n2 + 10n = 2n + -15

Reorder the terms:
10n + n2 = 2n + -15

Reorder the terms:
10n + n2 = -15 + 2n

Solving
10n + n2 = -15 + 2n

Solving for variable 'n'.

Reorder the terms:
15 + 10n + -2n + n2 = -15 + 2n + 15 + -2n

Combine like terms: 10n + -2n = 8n
15 + 8n + n2 = -15 + 2n + 15 + -2n

Reorder the terms:
15 + 8n + n2 = -15 + 15 + 2n + -2n

Combine like terms: -15 + 15 = 0
15 + 8n + n2 = 0 + 2n + -2n
15 + 8n + n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
15 + 8n + n2 = 0

Factor a trinomial.
(5 + n)(3 + n) = 0

Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Solution
n = {-5, -3}