(n-1)(n-6)=0

Solution for (n-1)(n-6)=0 equation:

Simplifying
(n + -1)(n + -6) = 0

Reorder the terms:
(-1 + n)(n + -6) = 0

Reorder the terms:
(-1 + n)(-6 + n) = 0

Multiply (-1 + n) * (-6 + n)
(-1(-6 + n) + n(-6 + n)) = 0
((-6 * -1 + n * -1) + n(-6 + n)) = 0
((6 + -1n) + n(-6 + n)) = 0
(6 + -1n + (-6 * n + n * n)) = 0
(6 + -1n + (-6n + n2)) = 0

Combine like terms: -1n + -6n = -7n
(6 + -7n + n2) = 0

Solving
6 + -7n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -1n)(6 + -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 '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {1, 6}