0=3t^2+8t+6

Solution for 0=3t^2+8t+6 equation:

Simplifying
0 = 3t2 + 8t + 6

Reorder the terms:
0 = 6 + 8t + 3t2

Solving
0 = 6 + 8t + 3t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + -8t + -3t2 = 6 + 8t + 3t2 + -6 + -8t + -3t2

Reorder the terms:
-6 + -8t + -3t2 = 6 + -6 + 8t + -8t + 3t2 + -3t2

Combine like terms: 6 + -6 = 0
-6 + -8t + -3t2 = 0 + 8t + -8t + 3t2 + -3t2
-6 + -8t + -3t2 = 8t + -8t + 3t2 + -3t2

Combine like terms: 8t + -8t = 0
-6 + -8t + -3t2 = 0 + 3t2 + -3t2
-6 + -8t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-6 + -8t + -3t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 8t + 3t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 8t + 3t2)' equal to zero and attempt to solve:

Simplifying
6 + 8t + 3t2 = 0

Solving
6 + 8t + 3t2 = 0

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

Divide each side by '3'.
2 + 2.666666667t + t2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2.666666667t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + 2.666666667t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2.666666667t + t2 = 0 + -2
2.666666667t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
2.666666667t + t2 = -2

The t term is 2.666666667t.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667t + 1.777777780 + t2 = -2 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667t + t2 = -2 + 1.777777780

Combine like terms: -2 + 1.777777780 = -0.22222222
1.777777780 + 2.666666667t + t2 = -0.22222222

Factor a perfect square on the left side:
(t + 1.333333334)(t + 1.333333334) = -0.22222222

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.