-5t^2+8t+6t^3-t^3+11t^2-6t=0

Solution for -5t^2+8t+6t^3-t^3+11t^2-6t=0 equation:

Simplifying
-5t2 + 8t + 6t3 + -1t3 + 11t2 + -6t = 0

Reorder the terms:
8t + -6t + -5t2 + 11t2 + 6t3 + -1t3 = 0

Combine like terms: 8t + -6t = 2t
2t + -5t2 + 11t2 + 6t3 + -1t3 = 0

Combine like terms: -5t2 + 11t2 = 6t2
2t + 6t2 + 6t3 + -1t3 = 0

Combine like terms: 6t3 + -1t3 = 5t3
2t + 6t2 + 5t3 = 0

Solving
2t + 6t2 + 5t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(2 + 6t + 5t2) = 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 '(2 + 6t + 5t2)' equal to zero and attempt to solve:

Simplifying
2 + 6t + 5t2 = 0

Solving
2 + 6t + 5t2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.4 + 1.2t + t2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 1.2t + -0.4 + t2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 1.2t + t2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 1.2t + t2 = 0 + -0.4
1.2t + t2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
1.2t + t2 = -0.4

The t term is 1.2t.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2t + 0.36 + t2 = -0.4 + 0.36

Reorder the terms:
0.36 + 1.2t + t2 = -0.4 + 0.36

Combine like terms: -0.4 + 0.36 = -0.04
0.36 + 1.2t + t2 = -0.04

Factor a perfect square on the left side:
(t + 0.6)(t + 0.6) = -0.04

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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