t^2=-48-14t

Solution for t^2=-48-14t equation:

Simplifying
t2 = -48 + -14t

Solving
t2 = -48 + -14t

Solving for variable 't'.

Reorder the terms:
48 + 14t + t2 = -48 + -14t + 48 + 14t

Reorder the terms:
48 + 14t + t2 = -48 + 48 + -14t + 14t

Combine like terms: -48 + 48 = 0
48 + 14t + t2 = 0 + -14t + 14t
48 + 14t + t2 = -14t + 14t

Combine like terms: -14t + 14t = 0
48 + 14t + t2 = 0

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

Subproblem 1
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
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}