3(4t^2-2t+1)+6=0

Solution for 3(4t^2-2t+1)+6=0 equation:

Simplifying
3(4t2 + -2t + 1) + 6 = 0

Reorder the terms:
3(1 + -2t + 4t2) + 6 = 0
(1 * 3 + -2t * 3 + 4t2 * 3) + 6 = 0
(3 + -6t + 12t2) + 6 = 0

Reorder the terms:
3 + 6 + -6t + 12t2 = 0

Combine like terms: 3 + 6 = 9
9 + -6t + 12t2 = 0

Solving
9 + -6t + 12t2 = 0

Solving for variable 't'.

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

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -2t + 4t2)' equal to zero and attempt to solve:

Simplifying
3 + -2t + 4t2 = 0

Solving
3 + -2t + 4t2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -0.5t + t2 = 0 + -0.75
-0.5t + t2 = 0 + -0.75

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

The t term is -0.5t.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5t + 0.0625 + t2 = -0.75 + 0.0625

Reorder the terms:
0.0625 + -0.5t + t2 = -0.75 + 0.0625

Combine like terms: -0.75 + 0.0625 = -0.6875
0.0625 + -0.5t + t2 = -0.6875

Factor a perfect square on the left side:
(t + -0.25)(t + -0.25) = -0.6875

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.

The solution to this equation could not be determined.