32=-16t^2+32t

Solution for 32=-16t^2+32t equation:

Simplifying
32 = -16t2 + 32t

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

Solving
32 = 32t + -16t2

Solving for variable 't'.

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

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

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

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

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

Simplifying
2 + -2t + t2 = 0

Solving
2 + -2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -2 + 1

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

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

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

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.