(7n-7)(3n-3)=0

Solution for (7n-7)(3n-3)=0 equation:

Simplifying
(7n + -7)(3n + -3) = 0

Reorder the terms:
(-7 + 7n)(3n + -3) = 0

Reorder the terms:
(-7 + 7n)(-3 + 3n) = 0

Multiply (-7 + 7n) * (-3 + 3n)
(-7(-3 + 3n) + 7n * (-3 + 3n)) = 0
((-3 * -7 + 3n * -7) + 7n * (-3 + 3n)) = 0
((21 + -21n) + 7n * (-3 + 3n)) = 0
(21 + -21n + (-3 * 7n + 3n * 7n)) = 0
(21 + -21n + (-21n + 21n2)) = 0

Combine like terms: -21n + -21n = -42n
(21 + -42n + 21n2) = 0

Solving
21 + -42n + 21n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '21'.
21(1 + -2n + n2) = 0

Factor a trinomial.
21((1 + -1n)(1 + -1n)) = 0

Ignore the factor 21.
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 '(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 = {1, 1}