256=144t-8t^2

Solution for 256=144t-8t^2 equation:

Simplifying
256 = 144t + -8t2

Solving
256 = 144t + -8t2

Solving for variable 't'.

Reorder the terms:
256 + -144t + 8t2 = 144t + -144t + -8t2 + 8t2

Combine like terms: 144t + -144t = 0
256 + -144t + 8t2 = 0 + -8t2 + 8t2
256 + -144t + 8t2 = -8t2 + 8t2

Combine like terms: -8t2 + 8t2 = 0
256 + -144t + 8t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(32 + -18t + t2) = 0

Factor a trinomial.
8((2 + -1t)(16 + -1t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

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

Simplifying
16 + -1t = 0

Solving
16 + -1t = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1t = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1t = 0 + -16
-1t = 0 + -16

Combine like terms: 0 + -16 = -16
-1t = -16

Divide each side by '-1'.
t = 16

Simplifying
t = 16
Solution
t = {2, 16}