(3t^2)+30t+48=0

Solution for (3t^2)+30t+48=0 equation:

Simplifying
(3t2) + 30t + 48 = 0

Reorder the terms:
48 + 30t + (3t2) = 0

Solving
48 + 30t + (3t2) = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + 10t + t2) = 0

Factor a trinomial.
3((8 + t)(2 + t)) = 0

Ignore the factor 3.
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 '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 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 + t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + t = 0 + -2
t = 0 + -2

Combine like terms: 0 + -2 = -2
t = -2

Simplifying
t = -2
Solution
t = {-8, -2}