16t^2+32t+768=0

Solution for 16t^2+32t+768=0 equation:

Simplifying
16t2 + 32t + 768 = 0

Reorder the terms:
768 + 32t + 16t2 = 0

Solving
768 + 32t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(48 + 2t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(48 + 2t + t2)' equal to zero and attempt to solve:

Simplifying
48 + 2t + t2 = 0

Solving
48 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + 2t + -48 + t2 = 0 + -48

Reorder the terms:
48 + -48 + 2t + t2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + 2t + t2 = 0 + -48
2t + t2 = 0 + -48

Combine like terms: 0 + -48 = -48
2t + t2 = -48

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 = -48 + 1

Reorder the terms:
1 + 2t + t2 = -48 + 1

Combine like terms: -48 + 1 = -47
1 + 2t + t2 = -47

Factor a perfect square on the left side:
(t + 1)(t + 1) = -47

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.