9t^3+t+4(t-3t^3)=

Solution for 9t^3+t+4(t-3t^3)= equation:

Simplifying
9t3 + t + 4(t + -3t3) = 0
9t3 + t + (t * 4 + -3t3 * 4) = 0
9t3 + t + (4t + -12t3) = 0

Reorder the terms:
t + 4t + 9t3 + -12t3 = 0

Combine like terms: t + 4t = 5t
5t + 9t3 + -12t3 = 0

Combine like terms: 9t3 + -12t3 = -3t3
5t + -3t3 = 0

Solving
5t + -3t3 = 0

Solving for variable 't'.

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

Simplifying
5 + -3t2 = 0

Solving
5 + -3t2 = 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 + -3t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3t2 = 0 + -5
-3t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-3t2 = -5

Divide each side by '-3'.
t2 = 1.666666667

Simplifying
t2 = 1.666666667

Take the square root of each side:
t = {-1.290994449, 1.290994449}
Solution
t = {0, -1.290994449, 1.290994449}