(N+5)N=150

Solution for (N+5)N=150 equation:

Simplifying
(N + 5) * N = 150

Reorder the terms:
(5 + N) * N = 150

Reorder the terms for easier multiplication:
N(5 + N) = 150
(5 * N + N * N) = 150
(5N + N2) = 150

Solving
5N + N2 = 150

Solving for variable 'N'.

Reorder the terms:
-150 + 5N + N2 = 150 + -150

Combine like terms: 150 + -150 = 0
-150 + 5N + N2 = 0

Factor a trinomial.
(-15 + -1N)(10 + -1N) = 0

Subproblem 1
Set the factor '(-15 + -1N)' equal to zero and attempt to solve:

Simplifying
-15 + -1N = 0

Solving
-15 + -1N = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1N = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1N = 0 + 15
-1N = 0 + 15

Combine like terms: 0 + 15 = 15
-1N = 15

Divide each side by '-1'.
N = -15

Simplifying
N = -15
Subproblem 2
Set the factor '(10 + -1N)' equal to zero and attempt to solve:

Simplifying
10 + -1N = 0

Solving
10 + -1N = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1N = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1N = 0 + -10
-1N = 0 + -10

Combine like terms: 0 + -10 = -10
-1N = -10

Divide each side by '-1'.
N = 10

Simplifying
N = 10
Solution
N = {-15, 10}