384=160t+16t^2

Solution for 384=160t+16t^2 equation:

Simplifying
384 = 160t + 16t2

Solving
384 = 160t + 16t2

Solving for variable 't'.

Reorder the terms:
384 + -160t + -16t2 = 160t + -160t + 16t2 + -16t2

Combine like terms: 160t + -160t = 0
384 + -160t + -16t2 = 0 + 16t2 + -16t2
384 + -160t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
384 + -160t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(24 + -10t + -1t2) = 0

Factor a trinomial.
16((2 + -1t)(12 + t)) = 0

Ignore the factor 16.
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 '(12 + t)' equal to zero and attempt to solve:

Simplifying
12 + t = 0

Solving
12 + t = 0

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

Add '-12' to each side of the equation.
12 + -12 + t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + t = 0 + -12
t = 0 + -12

Combine like terms: 0 + -12 = -12
t = -12

Simplifying
t = -12
Solution
t = {2, -12}