3t^3+t+5(t-9t^3)=

Solution for 3t^3+t+5(t-9t^3)= equation:

Simplifying
3t3 + t + 5(t + -9t3) = 0
3t3 + t + (t * 5 + -9t3 * 5) = 0
3t3 + t + (5t + -45t3) = 0

Reorder the terms:
t + 5t + 3t3 + -45t3 = 0

Combine like terms: t + 5t = 6t
6t + 3t3 + -45t3 = 0

Combine like terms: 3t3 + -45t3 = -42t3
6t + -42t3 = 0

Solving
6t + -42t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6t'.
6t(1 + -7t2) = 0

Ignore the factor 6.
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 + -7t2)' equal to zero and attempt to solve:

Simplifying
1 + -7t2 = 0

Solving
1 + -7t2 = 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 + -7t2 = 0 + -1

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

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

Divide each side by '-7'.
t2 = 0.1428571429

Simplifying
t2 = 0.1428571429

Take the square root of each side:
t = {-0.377964473, 0.377964473}
Solution
t = {0, -0.377964473, 0.377964473}