0=12(t^3+t^2+t)

Solution for 0=12(t^3+t^2+t) equation:

Simplifying
0 = 12(t3 + t2 + t)

Reorder the terms:
0 = 12(t + t2 + t3)
0 = (t * 12 + t2 * 12 + t3 * 12)
0 = (12t + 12t2 + 12t3)

Solving
0 = 12t + 12t2 + 12t3

Solving for variable 't'.
Remove the zero:
-12t + -12t2 + -12t3 = 12t + 12t2 + 12t3 + -12t + -12t2 + -12t3

Reorder the terms:
-12t + -12t2 + -12t3 = 12t + -12t + 12t2 + -12t2 + 12t3 + -12t3

Combine like terms: 12t + -12t = 0
-12t + -12t2 + -12t3 = 0 + 12t2 + -12t2 + 12t3 + -12t3
-12t + -12t2 + -12t3 = 12t2 + -12t2 + 12t3 + -12t3

Combine like terms: 12t2 + -12t2 = 0
-12t + -12t2 + -12t3 = 0 + 12t3 + -12t3
-12t + -12t2 + -12t3 = 12t3 + -12t3

Combine like terms: 12t3 + -12t3 = 0
-12t + -12t2 + -12t3 = 0

Factor out the Greatest Common Factor (GCF), '-12t'.
-12t(1 + t + t2) = 0

Ignore the factor -12.
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 + t + t2)' equal to zero and attempt to solve:

Simplifying
1 + t + t2 = 0

Solving
1 + t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + t + t2 = 0 + -1

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

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

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
t + 0.25 + t2 = -1 + 0.25

Reorder the terms:
0.25 + t + t2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + t + t2 = -0.75

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = -0.75

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}