4t^3+8t^2+12t=

Solution for 4t^3+8t^2+12t= equation:

Simplifying
4t3 + 8t2 + 12t = 0

Reorder the terms:
12t + 8t2 + 4t3 = 0

Solving
12t + 8t2 + 4t3 = 0

Solving for variable 't'.

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

Ignore the factor 4.
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 '(3 + 2t + t2)' equal to zero and attempt to solve:

Simplifying
3 + 2t + t2 = 0

Solving
3 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + 2t + t2 = 0 + -3

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

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

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = -3 + 1

Reorder the terms:
1 + 2t + t2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + 2t + t2 = -2

Factor a perfect square on the left side:
(t + 1)(t + 1) = -2

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}