(n^2-10)(n^2+10)=0

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Solution for (n^2-10)(n^2+10)=0 equation: 


Simplifying
(n2 + -10)(n2 + 10) = 0

Reorder the terms:
(-10 + n2)(n2 + 10) = 0

Reorder the terms:
(-10 + n2)(10 + n2) = 0

Multiply (-10 + n2) * (10 + n2)
(-10(10 + n2) + n2(10 + n2)) = 0
((10 * -10 + n2 * -10) + n2(10 + n2)) = 0
((-100 + -10n2) + n2(10 + n2)) = 0
(-100 + -10n2 + (10 * n2 + n2 * n2)) = 0
(-100 + -10n2 + (10n2 + n4)) = 0

Combine like terms: -10n2 + 10n2 = 0
(-100 + 0 + n4) = 0
(-100 + n4) = 0

Solving
-100 + n4 = 0

Solving for variable 'n'.

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

Add '100' to each side of the equation.
-100 + 100 + n4 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + n4 = 0 + 100
n4 = 0 + 100

Combine like terms: 0 + 100 = 100
n4 = 100

Simplifying
n4 = 100

Reorder the terms:
-100 + n4 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + n4 = 0

Factor a difference between two squares.
(10 + n2)(-10 + n2) = 0


Subproblem 1
Set the factor '(10 + n2)' equal to zero and attempt to solve:

Simplifying
10 + n2 = 0

Solving
10 + n2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + n2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + n2 = 0 + -10
n2 = 0 + -10

Combine like terms: 0 + -10 = -10
n2 = -10

Simplifying
n2 = -10

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 '(-10 + n2)' equal to zero and attempt to solve:

Simplifying
-10 + n2 = 0

Solving
-10 + n2 = 0

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

Add '10' to each side of the equation.
-10 + 10 + n2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + n2 = 0 + 10
n2 = 0 + 10

Combine like terms: 0 + 10 = 10
n2 = 10

Simplifying
n2 = 10

Take the square root of each side:
n = {-3.16227766, 3.16227766}
Solution
n = {-3.16227766, 3.16227766}

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