t^4+16t^2=225

Solution for t^4+16t^2=225 equation:

Simplifying
t4 + 16t2 = 225

Reorder the terms:
16t2 + t4 = 225

Solving
16t2 + t4 = 225

Solving for variable 't'.

Reorder the terms:
-225 + 16t2 + t4 = 225 + -225

Combine like terms: 225 + -225 = 0
-225 + 16t2 + t4 = 0

Factor a trinomial.
(-25 + -1t2)(9 + -1t2) = 0

Factor a difference between two squares.
(-25 + -1t2)((3 + t)(3 + -1t)) = 0

Subproblem 1
Set the factor '(-25 + -1t2)' equal to zero and attempt to solve:

Simplifying
-25 + -1t2 = 0

Solving
-25 + -1t2 = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1t2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1t2 = 0 + 25
-1t2 = 0 + 25

Combine like terms: 0 + 25 = 25
-1t2 = 25

Divide each side by '-1'.
t2 = -25

Simplifying
t2 = -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 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

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

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

Simplifying
t = -3
Subproblem 3
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

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

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

Divide each side by '-1'.
t = 3

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