16t^2+8t+54=6

Solution for 16t^2+8t+54=6 equation:

Simplifying
16t2 + 8t + 54 = 6

Reorder the terms:
54 + 8t + 16t2 = 6

Solving
54 + 8t + 16t2 = 6

Solving for variable 't'.

Reorder the terms:
54 + -6 + 8t + 16t2 = 6 + -6

Combine like terms: 54 + -6 = 48
48 + 8t + 16t2 = 6 + -6

Combine like terms: 6 + -6 = 0
48 + 8t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(6 + t + 2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(6 + t + 2t2)' equal to zero and attempt to solve:

Simplifying
6 + t + 2t2 = 0

Solving
6 + t + 2t2 = 0

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

Divide each side by '2'.
3 + 0.5t + t2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 0.5t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + 0.5t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 0.5t + t2 = 0 + -3
0.5t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
0.5t + t2 = -3

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.
0.5t + 0.25 + t2 = -3 + 0.25

Reorder the terms:
0.25 + 0.5t + t2 = -3 + 0.25

Combine like terms: -3 + 0.25 = -2.75
0.25 + 0.5t + t2 = -2.75

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = -2.75

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.

The solution to this equation could not be determined.