48=2t+t^2

Solution for 48=2t+t^2 equation:

Simplifying
48 = 2t + t2

Solving
48 = 2t + t2

Solving for variable 't'.

Reorder the terms:
48 + -2t + -1t2 = 2t + -2t + t2 + -1t2

Combine like terms: 2t + -2t = 0
48 + -2t + -1t2 = 0 + t2 + -1t2
48 + -2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
48 + -2t + -1t2 = 0

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

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

Simplifying
8 + t = 0

Solving
8 + t = 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 + t = 0 + -8

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

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

Simplifying
t = -8
Solution
t = {6, -8}