0=t^2-2t-48

Solution for 0=t^2-2t-48 equation:

Simplifying
0 = t2 + -2t + -48

Reorder the terms:
0 = -48 + -2t + t2

Solving
0 = -48 + -2t + t2

Solving for variable 't'.

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

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

Combine like terms: -48 + 48 = 0
48 + 2t + -1t2 = 0 + -2t + 2t + t2 + -1t2
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.
(8 + -1t)(6 + t) = 0

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

Simplifying
8 + -1t = 0

Solving
8 + -1t = 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 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
Subproblem 2
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 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 + t = 0 + -6

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

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

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