0=16t^2+32t+48

Solution for 0=16t^2+32t+48 equation:

Simplifying
0 = 16t2 + 32t + 48

Reorder the terms:
0 = 48 + 32t + 16t2

Solving
0 = 48 + 32t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -48 = -48
-48 + -32t + -16t2 = 48 + 32t + 16t2 + -48 + -32t + -16t2

Reorder the terms:
-48 + -32t + -16t2 = 48 + -48 + 32t + -32t + 16t2 + -16t2

Combine like terms: 48 + -48 = 0
-48 + -32t + -16t2 = 0 + 32t + -32t + 16t2 + -16t2
-48 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
-48 + -32t + -16t2 = 0 + 16t2 + -16t2
-48 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-48 + -32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-16'.
-16(3 + 2t + t2) = 0

Ignore the factor -16.
Subproblem 1
Set the factor '(3 + 2t + t2)' equal to zero and attempt to solve:

Simplifying
3 + 2t + t2 = 0

Solving
3 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + 2t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t + t2 = 0 + -3
2t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
2t + t2 = -3

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 = -3 + 1

Reorder the terms:
1 + 2t + t2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + 2t + t2 = -2

Factor a perfect square on the left side:
(t + 1)(t + 1) = -2

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.