a^4+16a^2-225=0

Solution for a^4+16a^2-225=0 equation:

Simplifying
a4 + 16a2 + -225 = 0

Reorder the terms:
-225 + 16a2 + a4 = 0

Solving
-225 + 16a2 + a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-25 + -1a2)(9 + -1a2) = 0

Factor a difference between two squares.
(-25 + -1a2)((3 + a)(3 + -1a)) = 0

Subproblem 1
Set the factor '(-25 + -1a2)' equal to zero and attempt to solve:

Simplifying
-25 + -1a2 = 0

Solving
-25 + -1a2 = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1a2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1a2 = 0 + 25
-1a2 = 0 + 25

Combine like terms: 0 + 25 = 25
-1a2 = 25

Divide each side by '-1'.
a2 = -25

Simplifying
a2 = -25

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 '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Subproblem 3
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-3, 3}