n*(n+5)-(n-3)=

Solution for n*(n+5)-(n-3)= equation:

Simplifying
n(n + 5) + -1(n + -3) = 0

Reorder the terms:
n(5 + n) + -1(n + -3) = 0
(5 * n + n * n) + -1(n + -3) = 0
(5n + n2) + -1(n + -3) = 0

Reorder the terms:
5n + n2 + -1(-3 + n) = 0
5n + n2 + (-3 * -1 + n * -1) = 0
5n + n2 + (3 + -1n) = 0

Reorder the terms:
3 + 5n + -1n + n2 = 0

Combine like terms: 5n + -1n = 4n
3 + 4n + n2 = 0

Solving
3 + 4n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + n)(1 + n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {-3, -1}