t^5-10t^3+21t=0

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Solution for t^5-10t^3+21t=0 equation: 


Simplifying
t5 + -10t3 + 21t = 0

Reorder the terms:
21t + -10t3 + t5 = 0

Solving
21t + -10t3 + t5 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(21 + -10t2 + t4) = 0

Factor a trinomial.
t((3 + -1t2)(7 + -1t2)) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0

Subproblem 2
Set the factor '(3 + -1t2)' equal to zero and attempt to solve:

Simplifying
3 + -1t2 = 0

Solving
3 + -1t2 = 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 + -1t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t2 = 0 + -3
-1t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1t2 = -3

Divide each side by '-1'.
t2 = 3

Simplifying
t2 = 3

Take the square root of each side:
t = {-1.732050808, 1.732050808}

Subproblem 3
Set the factor '(7 + -1t2)' equal to zero and attempt to solve:

Simplifying
7 + -1t2 = 0

Solving
7 + -1t2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t2 = 0 + -7
-1t2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1t2 = -7

Divide each side by '-1'.
t2 = 7

Simplifying
t2 = 7

Take the square root of each side:
t = {-2.645751311, 2.645751311}
Solution
t = {0, -1.732050808, 1.732050808, -2.645751311, 2.645751311}

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