3(t)=64t-64t^2

Solution for 3(t)=64t-64t^2 equation:

Simplifying
3(t) = 64t + -64t2

Solving
3t = 64t + -64t2

Solving for variable 't'.

Combine like terms: 3t + -64t = -61t
-61t + 64t2 = 64t + -64t2 + -64t + 64t2

Reorder the terms:
-61t + 64t2 = 64t + -64t + -64t2 + 64t2

Combine like terms: 64t + -64t = 0
-61t + 64t2 = 0 + -64t2 + 64t2
-61t + 64t2 = -64t2 + 64t2

Combine like terms: -64t2 + 64t2 = 0
-61t + 64t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-61 + 64t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(-61 + 64t)' equal to zero and attempt to solve:

Simplifying
-61 + 64t = 0

Solving
-61 + 64t = 0

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

Add '61' to each side of the equation.
-61 + 61 + 64t = 0 + 61

Combine like terms: -61 + 61 = 0
0 + 64t = 0 + 61
64t = 0 + 61

Combine like terms: 0 + 61 = 61
64t = 61

Divide each side by '64'.
t = 0.953125

Simplifying
t = 0.953125
Solution
t = {0, 0.953125}