(n-4)*(n-4)=100

Solution for (n-4)*(n-4)=100 equation:

Simplifying
(n + -4)(n + -4) = 100

Reorder the terms:
(-4 + n)(n + -4) = 100

Reorder the terms:
(-4 + n)(-4 + n) = 100

Multiply (-4 + n) * (-4 + n)
(-4(-4 + n) + n(-4 + n)) = 100
((-4 * -4 + n * -4) + n(-4 + n)) = 100
((16 + -4n) + n(-4 + n)) = 100
(16 + -4n + (-4 * n + n * n)) = 100
(16 + -4n + (-4n + n2)) = 100

Combine like terms: -4n + -4n = -8n
(16 + -8n + n2) = 100

Solving
16 + -8n + n2 = 100

Solving for variable 'n'.

Reorder the terms:
16 + -100 + -8n + n2 = 100 + -100

Combine like terms: 16 + -100 = -84
-84 + -8n + n2 = 100 + -100

Combine like terms: 100 + -100 = 0
-84 + -8n + n2 = 0

Factor a trinomial.
(-6 + -1n)(14 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {-6, 14}