n(n-3)+2(n-3)=(n-3)

Solution for n(n-3)+2(n-3)=(n-3) equation:

Simplifying
n(n + -3) + 2(n + -3) = (n + -3)

Reorder the terms:
n(-3 + n) + 2(n + -3) = (n + -3)
(-3 * n + n * n) + 2(n + -3) = (n + -3)
(-3n + n2) + 2(n + -3) = (n + -3)

Reorder the terms:
-3n + n2 + 2(-3 + n) = (n + -3)
-3n + n2 + (-3 * 2 + n * 2) = (n + -3)
-3n + n2 + (-6 + 2n) = (n + -3)

Reorder the terms:
-6 + -3n + 2n + n2 = (n + -3)

Combine like terms: -3n + 2n = -1n
-6 + -1n + n2 = (n + -3)

Reorder the terms:
-6 + -1n + n2 = (-3 + n)

Remove parenthesis around (-3 + n)
-6 + -1n + n2 = -3 + n

Solving
-6 + -1n + n2 = -3 + n

Solving for variable 'n'.

Reorder the terms:
-6 + 3 + -1n + -1n + n2 = -3 + n + 3 + -1n

Combine like terms: -6 + 3 = -3
-3 + -1n + -1n + n2 = -3 + n + 3 + -1n

Combine like terms: -1n + -1n = -2n
-3 + -2n + n2 = -3 + n + 3 + -1n

Reorder the terms:
-3 + -2n + n2 = -3 + 3 + n + -1n

Combine like terms: -3 + 3 = 0
-3 + -2n + n2 = 0 + n + -1n
-3 + -2n + n2 = n + -1n

Combine like terms: n + -1n = 0
-3 + -2n + n2 = 0

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

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

Simplifying
-1 + -1n = 0

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

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

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

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

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