6t^2+102t+312=0

Solution for 6t^2+102t+312=0 equation:

Simplifying
6t2 + 102t + 312 = 0

Reorder the terms:
312 + 102t + 6t2 = 0

Solving
312 + 102t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(52 + 17t + t2) = 0

Factor a trinomial.
6((13 + t)(4 + t)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(13 + t)' equal to zero and attempt to solve:

Simplifying
13 + t = 0

Solving
13 + t = 0

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

Add '-13' to each side of the equation.
13 + -13 + t = 0 + -13

Combine like terms: 13 + -13 = 0
0 + t = 0 + -13
t = 0 + -13

Combine like terms: 0 + -13 = -13
t = -13

Simplifying
t = -13
Subproblem 2
Set the factor '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 0

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

Add '-4' to each side of the equation.
4 + -4 + t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t = 0 + -4
t = 0 + -4

Combine like terms: 0 + -4 = -4
t = -4

Simplifying
t = -4
Solution
t = {-13, -4}