5t^3+t+3(t-3t^3)=

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

Simplifying
5t3 + t + 3(t + -3t3) = 0
5t3 + t + (t * 3 + -3t3 * 3) = 0
5t3 + t + (3t + -9t3) = 0

Reorder the terms:
t + 3t + 5t3 + -9t3 = 0

Combine like terms: t + 3t = 4t
4t + 5t3 + -9t3 = 0

Combine like terms: 5t3 + -9t3 = -4t3
4t + -4t3 = 0

Solving
4t + -4t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4t'.
4t(1 + -1t2) = 0

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

Ignore the factor 4.
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 '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

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

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

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1t = 0 + -1

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

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

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

Simplifying
t = 1
Solution
t = {0, -1, 1}