-9t^2+10t+5t^3-t^3+14t^2-4t=

Solution for -9t^2+10t+5t^3-t^3+14t^2-4t= equation:

Simplifying
-9t2 + 10t + 5t3 + -1t3 + 14t2 + -4t = 0

Reorder the terms:
10t + -4t + -9t2 + 14t2 + 5t3 + -1t3 = 0

Combine like terms: 10t + -4t = 6t
6t + -9t2 + 14t2 + 5t3 + -1t3 = 0

Combine like terms: -9t2 + 14t2 = 5t2
6t + 5t2 + 5t3 + -1t3 = 0

Combine like terms: 5t3 + -1t3 = 4t3
6t + 5t2 + 4t3 = 0

Solving
6t + 5t2 + 4t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(6 + 5t + 4t2) = 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 '(6 + 5t + 4t2)' equal to zero and attempt to solve:

Simplifying
6 + 5t + 4t2 = 0

Solving
6 + 5t + 4t2 = 0

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

Divide each side by '4'.
1.5 + 1.25t + t2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 1.25t + -1.5 + t2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 1.25t + t2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 1.25t + t2 = 0 + -1.5
1.25t + t2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
1.25t + t2 = -1.5

The t term is 1.25t.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25t + 0.390625 + t2 = -1.5 + 0.390625

Reorder the terms:
0.390625 + 1.25t + t2 = -1.5 + 0.390625

Combine like terms: -1.5 + 0.390625 = -1.109375
0.390625 + 1.25t + t2 = -1.109375

Factor a perfect square on the left side:
(t + 0.625)(t + 0.625) = -1.109375

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}