(n-1)(n+1)-90.33=0

Solution for (n-1)(n+1)-90.33=0 equation:

Simplifying
(n + -1)(n + 1) + -90.33 = 0

Reorder the terms:
(-1 + n)(n + 1) + -90.33 = 0

Reorder the terms:
(-1 + n)(1 + n) + -90.33 = 0

Multiply (-1 + n) * (1 + n)
(-1(1 + n) + n(1 + n)) + -90.33 = 0
((1 * -1 + n * -1) + n(1 + n)) + -90.33 = 0
((-1 + -1n) + n(1 + n)) + -90.33 = 0
(-1 + -1n + (1 * n + n * n)) + -90.33 = 0
(-1 + -1n + (1n + n2)) + -90.33 = 0

Combine like terms: -1n + 1n = 0
(-1 + 0 + n2) + -90.33 = 0
(-1 + n2) + -90.33 = 0

Reorder the terms:
-1 + -90.33 + n2 = 0

Combine like terms: -1 + -90.33 = -91.33
-91.33 + n2 = 0

Solving
-91.33 + n2 = 0

Solving for variable 'n'.

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

Add '91.33' to each side of the equation.
-91.33 + 91.33 + n2 = 0 + 91.33

Combine like terms: -91.33 + 91.33 = 0.00
0.00 + n2 = 0 + 91.33
n2 = 0 + 91.33

Combine like terms: 0 + 91.33 = 91.33
n2 = 91.33

Simplifying
n2 = 91.33

Take the square root of each side:
n = {-9.556673061, 9.556673061}