X(t)=3t^5+5t^3+23t^2-t^2

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Solution for X(t)=3t^5+5t^3+23t^2-t^2 equation: 


Simplifying
X(t) = 3t5 + 5t3 + 23t2 + -1t2

Multiply X * t
tX = 3t5 + 5t3 + 23t2 + -1t2

Reorder the terms:
tX = 23t2 + -1t2 + 5t3 + 3t5

Combine like terms: 23t2 + -1t2 = 22t2
tX = 22t2 + 5t3 + 3t5

Solving
tX = 22t2 + 5t3 + 3t5

Solving for variable 't'.

Reorder the terms:
tX + -22t2 + -5t3 + -3t5 = 22t2 + -22t2 + 5t3 + -5t3 + 3t5 + -3t5

Combine like terms: 22t2 + -22t2 = 0
tX + -22t2 + -5t3 + -3t5 = 0 + 5t3 + -5t3 + 3t5 + -3t5
tX + -22t2 + -5t3 + -3t5 = 5t3 + -5t3 + 3t5 + -3t5

Combine like terms: 5t3 + -5t3 = 0
tX + -22t2 + -5t3 + -3t5 = 0 + 3t5 + -3t5
tX + -22t2 + -5t3 + -3t5 = 3t5 + -3t5

Combine like terms: 3t5 + -3t5 = 0
tX + -22t2 + -5t3 + -3t5 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(X + -22t + -5t2 + -3t4) = 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 '(X + -22t + -5t2 + -3t4)' equal to zero and attempt to solve:

Simplifying
X + -22t + -5t2 + -3t4 = 0

Solving
X + -22t + -5t2 + -3t4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {0}

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