15t^4-45t^2=60

Solution for 15t^4-45t^2=60 equation:

Simplifying
15t4 + -45t2 = 60

Reorder the terms:
-45t2 + 15t4 = 60

Solving
-45t2 + 15t4 = 60

Solving for variable 't'.

Reorder the terms:
-60 + -45t2 + 15t4 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -45t2 + 15t4 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-4 + -3t2 + t4) = 0

Factor a trinomial.
15((-1 + -1t2)(4 + -1t2)) = 0

Factor a difference between two squares.
15((-1 + -1t2)((2 + t)(2 + -1t))) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-1 + -1t2)' equal to zero and attempt to solve:

Simplifying
-1 + -1t2 = 0

Solving
-1 + -1t2 = 0

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

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

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

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

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

Simplifying
t2 = -1

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 '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 0

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

Add '-2' to each side of the equation.
2 + -2 + t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + t = 0 + -2
t = 0 + -2

Combine like terms: 0 + -2 = -2
t = -2

Simplifying
t = -2
Subproblem 3
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-2, 2}