0=4t^3+3t^2+2t

Solution for 0=4t^3+3t^2+2t equation:

Simplifying
0 = 4t3 + 3t2 + 2t

Reorder the terms:
0 = 2t + 3t2 + 4t3

Solving
0 = 2t + 3t2 + 4t3

Solving for variable 't'.
Remove the zero:
-2t + -3t2 + -4t3 = 2t + 3t2 + 4t3 + -2t + -3t2 + -4t3

Reorder the terms:
-2t + -3t2 + -4t3 = 2t + -2t + 3t2 + -3t2 + 4t3 + -4t3

Combine like terms: 2t + -2t = 0
-2t + -3t2 + -4t3 = 0 + 3t2 + -3t2 + 4t3 + -4t3
-2t + -3t2 + -4t3 = 3t2 + -3t2 + 4t3 + -4t3

Combine like terms: 3t2 + -3t2 = 0
-2t + -3t2 + -4t3 = 0 + 4t3 + -4t3
-2t + -3t2 + -4t3 = 4t3 + -4t3

Combine like terms: 4t3 + -4t3 = 0
-2t + -3t2 + -4t3 = 0

Factor out the Greatest Common Factor (GCF), '-1t'.
-1t(2 + 3t + 4t2) = 0

Ignore the factor -1.
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 + 3t + 4t2)' equal to zero and attempt to solve:

Simplifying
2 + 3t + 4t2 = 0

Solving
2 + 3t + 4t2 = 0

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

Divide each side by '4'.
0.5 + 0.75t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.75t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.75t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.75t + t2 = 0 + -0.5
0.75t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.75t + t2 = -0.5

The t term is 0.75t.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75t + 0.140625 + t2 = -0.5 + 0.140625

Reorder the terms:
0.140625 + 0.75t + t2 = -0.5 + 0.140625

Combine like terms: -0.5 + 0.140625 = -0.359375
0.140625 + 0.75t + t2 = -0.359375

Factor a perfect square on the left side:
(t + 0.375)(t + 0.375) = -0.359375

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}