4t^3+t+4(t-6t^3)=

Solution for 4t^3+t+4(t-6t^3)= equation:

Simplifying
4t3 + t + 4(t + -6t3) = 0
4t3 + t + (t * 4 + -6t3 * 4) = 0
4t3 + t + (4t + -24t3) = 0

Reorder the terms:
t + 4t + 4t3 + -24t3 = 0

Combine like terms: t + 4t = 5t
5t + 4t3 + -24t3 = 0

Combine like terms: 4t3 + -24t3 = -20t3
5t + -20t3 = 0

Solving
5t + -20t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5t'.
5t(1 + -4t2) = 0

Factor a difference between two squares.
5t((1 + 2t)(1 + -2t)) = 0

Ignore the factor 5.
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 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Subproblem 3
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {0, -0.5, 0.5}