-5t^2-10t+105=0

Solution for -5t^2-10t+105=0 equation:

Simplifying
-5t2 + -10t + 105 = 0

Reorder the terms:
105 + -10t + -5t2 = 0

Solving
105 + -10t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(21 + -2t + -1t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(21 + -2t + -1t2)' equal to zero and attempt to solve:

Simplifying
21 + -2t + -1t2 = 0

Solving
21 + -2t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-21 + 2t + t2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 2t + 21 + t2 = 0 + 21

Reorder the terms:
-21 + 21 + 2t + t2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2t + t2 = 0 + 21
2t + t2 = 0 + 21

Combine like terms: 0 + 21 = 21
2t + t2 = 21

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 21 + 1

Reorder the terms:
1 + 2t + t2 = 21 + 1

Combine like terms: 21 + 1 = 22
1 + 2t + t2 = 22

Factor a perfect square on the left side:
(t + 1)(t + 1) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(t + 1) equal to 4.69041576 and -4.69041576.

Subproblem 1
t + 1 = 4.69041576

Simplifying
t + 1 = 4.69041576

Reorder the terms:
1 + t = 4.69041576

Solving
1 + t = 4.69041576

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 4.69041576 + -1

Combine like terms: 1 + -1 = 0
0 + t = 4.69041576 + -1
t = 4.69041576 + -1

Combine like terms: 4.69041576 + -1 = 3.69041576
t = 3.69041576

Simplifying
t = 3.69041576

Subproblem 2
t + 1 = -4.69041576

Simplifying
t + 1 = -4.69041576

Reorder the terms:
1 + t = -4.69041576

Solving
1 + t = -4.69041576

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -4.69041576 + -1

Combine like terms: 1 + -1 = 0
0 + t = -4.69041576 + -1
t = -4.69041576 + -1

Combine like terms: -4.69041576 + -1 = -5.69041576
t = -5.69041576

Simplifying
t = -5.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.69041576, -5.69041576}
Solution
t = {3.69041576, -5.69041576}