(t^2-4)(4t^2+16)=0

Solution for (t^2-4)(4t^2+16)=0 equation:

Simplifying
(t2 + -4)(4t2 + 16) = 0

Reorder the terms:
(-4 + t2)(4t2 + 16) = 0

Reorder the terms:
(-4 + t2)(16 + 4t2) = 0

Multiply (-4 + t2) * (16 + 4t2)
(-4(16 + 4t2) + t2(16 + 4t2)) = 0
((16 * -4 + 4t2 * -4) + t2(16 + 4t2)) = 0
((-64 + -16t2) + t2(16 + 4t2)) = 0
(-64 + -16t2 + (16 * t2 + 4t2 * t2)) = 0
(-64 + -16t2 + (16t2 + 4t4)) = 0

Combine like terms: -16t2 + 16t2 = 0
(-64 + 0 + 4t4) = 0
(-64 + 4t4) = 0

Solving
-64 + 4t4 = 0

Solving for variable 't'.

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

Add '64' to each side of the equation.
-64 + 64 + 4t4 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 4t4 = 0 + 64
4t4 = 0 + 64

Combine like terms: 0 + 64 = 64
4t4 = 64

Divide each side by '4'.
t4 = 16

Simplifying
t4 = 16

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

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

Factor a difference between two squares.
(4 + t2)(-4 + t2) = 0

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

Subproblem 1
Set the factor '(4 + t2)' equal to zero and attempt to solve:

Simplifying
4 + t2 = 0

Solving
4 + t2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + t2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t2 = 0 + -4
t2 = 0 + -4

Combine like terms: 0 + -4 = -4
t2 = -4

Simplifying
t2 = -4

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 + 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
Solution
t = {-2, 2}