16t^4-80=1

Solution for 16t^4-80=1 equation:

Simplifying
16t4 + -80 = 1

Reorder the terms:
-80 + 16t4 = 1

Solving
-80 + 16t4 = 1

Solving for variable 't'.

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

Add '80' to each side of the equation.
-80 + 80 + 16t4 = 1 + 80

Combine like terms: -80 + 80 = 0
0 + 16t4 = 1 + 80
16t4 = 1 + 80

Combine like terms: 1 + 80 = 81
16t4 = 81

Divide each side by '16'.
t4 = 5.0625

Simplifying
t4 = 5.0625

Reorder the terms:
-5.0625 + t4 = 5.0625 + -5.0625

Combine like terms: 5.0625 + -5.0625 = 0.0000
-5.0625 + t4 = 0.0000

Factor a difference between two squares.
(2.25 + t2)(-2.25 + t2) = 0.0000

Factor a difference between two squares.
(2.25 + t2)((1.5 + t)(-1.5 + t)) = 0.0000

Subproblem 1
Set the factor '(2.25 + t2)' equal to zero and attempt to solve:

Simplifying
2.25 + t2 = 0

Solving
2.25 + t2 = 0

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t2 = 0 + -2.25
t2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
t2 = -2.25

Simplifying
t2 = -2.25

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

Simplifying
1.5 + t = 0

Solving
1.5 + t = 0

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 0 + -1.5
t = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
t = -1.5

Simplifying
t = -1.5
Subproblem 3
Set the factor '(-1.5 + t)' equal to zero and attempt to solve:

Simplifying
-1.5 + t = 0

Solving
-1.5 + t = 0

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 0 + 1.5
t = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
t = 1.5

Simplifying
t = 1.5
Solution
t = {-1.5, 1.5}