3(n-1)=n(n-1)

Solution for 3(n-1)=n(n-1) equation:

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

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

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

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

Solving for variable 'n'.

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

Reorder the terms:
-3 + 4n + -1n2 = -1n + n + n2 + -1n2

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

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

Factor a trinomial.
(-3 + n)(1 + -1n) = 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 + -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
Solution
n = {3, 1}