6t^2+420t-3549=0

Solution for 6t^2+420t-3549=0 equation:

Simplifying
6t2 + 420t + -3549 = 0

Reorder the terms:
-3549 + 420t + 6t2 = 0

Solving
-3549 + 420t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1183 + 140t + 2t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1183 + 140t + 2t2)' equal to zero and attempt to solve:

Simplifying
-1183 + 140t + 2t2 = 0

Solving
-1183 + 140t + 2t2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-591.5 + 70t + t2 = 0

Move the constant term to the right:

Add '591.5' to each side of the equation.
-591.5 + 70t + 591.5 + t2 = 0 + 591.5

Reorder the terms:
-591.5 + 591.5 + 70t + t2 = 0 + 591.5

Combine like terms: -591.5 + 591.5 = 0.0
0.0 + 70t + t2 = 0 + 591.5
70t + t2 = 0 + 591.5

Combine like terms: 0 + 591.5 = 591.5
70t + t2 = 591.5

The t term is 70t.  Take half its coefficient (35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
70t + 1225 + t2 = 591.5 + 1225

Reorder the terms:
1225 + 70t + t2 = 591.5 + 1225

Combine like terms: 591.5 + 1225 = 1816.5
1225 + 70t + t2 = 1816.5

Factor a perfect square on the left side:
(t + 35)(t + 35) = 1816.5

Calculate the square root of the right side: 42.620417642

Break this problem into two subproblems by setting 
(t + 35) equal to 42.620417642 and -42.620417642.

Subproblem 1
t + 35 = 42.620417642

Simplifying
t + 35 = 42.620417642

Reorder the terms:
35 + t = 42.620417642

Solving
35 + t = 42.620417642

Solving for variable 't'.

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

Add '-35' to each side of the equation.
35 + -35 + t = 42.620417642 + -35

Combine like terms: 35 + -35 = 0
0 + t = 42.620417642 + -35
t = 42.620417642 + -35

Combine like terms: 42.620417642 + -35 = 7.620417642
t = 7.620417642

Simplifying
t = 7.620417642

Subproblem 2
t + 35 = -42.620417642

Simplifying
t + 35 = -42.620417642

Reorder the terms:
35 + t = -42.620417642

Solving
35 + t = -42.620417642

Solving for variable 't'.

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

Add '-35' to each side of the equation.
35 + -35 + t = -42.620417642 + -35

Combine like terms: 35 + -35 = 0
0 + t = -42.620417642 + -35
t = -42.620417642 + -35

Combine like terms: -42.620417642 + -35 = -77.620417642
t = -77.620417642

Simplifying
t = -77.620417642

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.620417642, -77.620417642}
Solution
t = {7.620417642, -77.620417642}