6t^4+6t^3+6t^2=

Solution for 6t^4+6t^3+6t^2= equation:

Simplifying
6t4 + 6t3 + 6t2 = 0

Reorder the terms:
6t2 + 6t3 + 6t4 = 0

Solving
6t2 + 6t3 + 6t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6t2'.
6t2(1 + t + t2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 't2' equal to zero and attempt to solve:

Simplifying
t2 = 0

Solving
t2 = 0

Move all terms containing t to the left, all other terms to the right.

Simplifying
t2 = 0

Take the square root of each side:
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}