48=38t-5t^2

Solution for 48=38t-5t^2 equation:

Simplifying
48 = 38t + -5t2

Solving
48 = 38t + -5t2

Solving for variable 't'.

Reorder the terms:
48 + -38t + 5t2 = 38t + -38t + -5t2 + 5t2

Combine like terms: 38t + -38t = 0
48 + -38t + 5t2 = 0 + -5t2 + 5t2
48 + -38t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
48 + -38t + 5t2 = 0

Factor a trinomial.
(8 + -5t)(6 + -1t) = 0

Subproblem 1
Set the factor '(8 + -5t)' equal to zero and attempt to solve:

Simplifying
8 + -5t = 0

Solving
8 + -5t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5t = 0 + -8
-5t = 0 + -8

Combine like terms: 0 + -8 = -8
-5t = -8

Divide each side by '-5'.
t = 1.6

Simplifying
t = 1.6
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {1.6, 6}