0(t)=-16t^2+48t+64

Solution for 0(t)=-16t^2+48t+64 equation:

Simplifying
0(t) = -16t2 + 48t + 64

Anything times zero is zero.
0t = -16t2 + 48t + 64

Reorder the terms:
0 = 64 + 48t + -16t2

Solving
0 = 64 + 48t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -64 = -64
-64 + -48t + 16t2 = 64 + 48t + -16t2 + -64 + -48t + 16t2

Reorder the terms:
-64 + -48t + 16t2 = 64 + -64 + 48t + -48t + -16t2 + 16t2

Combine like terms: 64 + -64 = 0
-64 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2
-64 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
-64 + -48t + 16t2 = 0 + -16t2 + 16t2
-64 + -48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-64 + -48t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-4 + -3t + t2) = 0

Factor a trinomial.
16((-1 + -1t)(4 + -1t)) = 0

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

Simplifying
-1 + -1t = 0

Solving
-1 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1t = 0 + 1
-1t = 0 + 1

Combine like terms: 0 + 1 = 1
-1t = 1

Divide each side by '-1'.
t = -1

Simplifying
t = -1
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-1, 4}