n(n-3)+8(n-3)=0

Solution for n(n-3)+8(n-3)=0 equation:

Simplifying
n(n + -3) + 8(n + -3) = 0

Reorder the terms:
n(-3 + n) + 8(n + -3) = 0
(-3 * n + n * n) + 8(n + -3) = 0
(-3n + n2) + 8(n + -3) = 0

Reorder the terms:
-3n + n2 + 8(-3 + n) = 0
-3n + n2 + (-3 * 8 + n * 8) = 0
-3n + n2 + (-24 + 8n) = 0

Reorder the terms:
-24 + -3n + 8n + n2 = 0

Combine like terms: -3n + 8n = 5n
-24 + 5n + n2 = 0

Solving
-24 + 5n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-8 + -1n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-8, 3}