t^4+80=21t^2

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Solution for t^4+80=21t^2 equation: 


Simplifying
t4 + 80 = 21t2

Reorder the terms:
80 + t4 = 21t2

Solving
80 + t4 = 21t2

Solving for variable 't'.

Reorder the terms:
80 + -21t2 + t4 = 21t2 + -21t2

Combine like terms: 21t2 + -21t2 = 0
80 + -21t2 + t4 = 0

Factor a trinomial.
(5 + -1t2)(16 + -1t2) = 0

Factor a difference between two squares.
(5 + -1t2)((4 + t)(4 + -1t)) = 0


Subproblem 1
Set the factor '(5 + -1t2)' equal to zero and attempt to solve:

Simplifying
5 + -1t2 = 0

Solving
5 + -1t2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t2 = 0 + -5
-1t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1t2 = -5

Divide each side by '-1'.
t2 = 5

Simplifying
t2 = 5

Take the square root of each side:
t = {-2.236067978, 2.236067978}

Subproblem 2
Set the factor '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 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 + t = 0 + -4

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

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

Simplifying
t = -4

Subproblem 3
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 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 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-2.236067978, 2.236067978, -4, 4}

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