n^4-170n^2+169=0

Solution for n^4-170n^2+169=0 equation:

Simplifying
n4 + -170n2 + 169 = 0

Reorder the terms:
169 + -170n2 + n4 = 0

Solving
169 + -170n2 + n4 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -1n2)(169 + -1n2) = 0

Factor a difference between two squares.
((1 + n)(1 + -1n))(169 + -1n2) = 0

Factor a difference between two squares.
((13 + n)(13 + -1n))(1 + n)(1 + -1n) = 0

Subproblem 1
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 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
Subproblem 3
Set the factor '(13 + n)' equal to zero and attempt to solve:

Simplifying
13 + n = 0

Solving
13 + n = 0

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

Add '-13' to each side of the equation.
13 + -13 + n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + n = 0 + -13
n = 0 + -13

Combine like terms: 0 + -13 = -13
n = -13

Simplifying
n = -13
Subproblem 4
Set the factor '(13 + -1n)' equal to zero and attempt to solve:

Simplifying
13 + -1n = 0

Solving
13 + -1n = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1n = 0 + -13
-1n = 0 + -13

Combine like terms: 0 + -13 = -13
-1n = -13

Divide each side by '-1'.
n = 13

Simplifying
n = 13
Solution
n = {-1, 1, -13, 13}