(n^2-1)(n^2+20)=

Solution for (n^2-1)(n^2+20)= equation:

Simplifying
(n2 + -1)(n2 + 20) = 0

Reorder the terms:
(-1 + n2)(n2 + 20) = 0

Reorder the terms:
(-1 + n2)(20 + n2) = 0

Multiply (-1 + n2) * (20 + n2)
(-1(20 + n2) + n2(20 + n2)) = 0
((20 * -1 + n2 * -1) + n2(20 + n2)) = 0
((-20 + -1n2) + n2(20 + n2)) = 0
(-20 + -1n2 + (20 * n2 + n2 * n2)) = 0
(-20 + -1n2 + (20n2 + n4)) = 0

Combine like terms: -1n2 + 20n2 = 19n2
(-20 + 19n2 + n4) = 0

Solving
-20 + 19n2 + n4 = 0

Solving for variable 'n'.

Factor a trinomial.
(-20 + -1n2)(1 + -1n2) = 0

Factor a difference between two squares.
(-20 + -1n2)((1 + n)(1 + -1n)) = 0

Subproblem 1
Set the factor '(-20 + -1n2)' equal to zero and attempt to solve:

Simplifying
-20 + -1n2 = 0

Solving
-20 + -1n2 = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1n2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1n2 = 0 + 20
-1n2 = 0 + 20

Combine like terms: 0 + 20 = 20
-1n2 = 20

Divide each side by '-1'.
n2 = -20

Simplifying
n2 = -20

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 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 + n = 0 + -1

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

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

Simplifying
n = -1
Subproblem 3
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}