3t^2-36t-105=0

Solution for 3t^2-36t-105=0 equation:

Simplifying
3t2 + -36t + -105 = 0

Reorder the terms:
-105 + -36t + 3t2 = 0

Solving
-105 + -36t + 3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + -12t + t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-35 + -12t + t2)' equal to zero and attempt to solve:

Simplifying
-35 + -12t + t2 = 0

Solving
-35 + -12t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -12t + 35 + t2 = 0 + 35

Reorder the terms:
-35 + 35 + -12t + t2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -12t + t2 = 0 + 35
-12t + t2 = 0 + 35

Combine like terms: 0 + 35 = 35
-12t + t2 = 35

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = 35 + 36

Reorder the terms:
36 + -12t + t2 = 35 + 36

Combine like terms: 35 + 36 = 71
36 + -12t + t2 = 71

Factor a perfect square on the left side:
(t + -6)(t + -6) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(t + -6) equal to 8.426149773 and -8.426149773.

Subproblem 1
t + -6 = 8.426149773

Simplifying
t + -6 = 8.426149773

Reorder the terms:
-6 + t = 8.426149773

Solving
-6 + t = 8.426149773

Solving for variable 't'.

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 = 8.426149773 + 6

Combine like terms: -6 + 6 = 0
0 + t = 8.426149773 + 6
t = 8.426149773 + 6

Combine like terms: 8.426149773 + 6 = 14.426149773
t = 14.426149773

Simplifying
t = 14.426149773

Subproblem 2
t + -6 = -8.426149773

Simplifying
t + -6 = -8.426149773

Reorder the terms:
-6 + t = -8.426149773

Solving
-6 + t = -8.426149773

Solving for variable 't'.

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 = -8.426149773 + 6

Combine like terms: -6 + 6 = 0
0 + t = -8.426149773 + 6
t = -8.426149773 + 6

Combine like terms: -8.426149773 + 6 = -2.426149773
t = -2.426149773

Simplifying
t = -2.426149773

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.426149773, -2.426149773}
Solution
t = {14.426149773, -2.426149773}