-15t^2+105t+10=-190

Solution for -15t^2+105t+10=-190 equation:

Simplifying
-15t2 + 105t + 10 = -190

Reorder the terms:
10 + 105t + -15t2 = -190

Solving
10 + 105t + -15t2 = -190

Solving for variable 't'.

Reorder the terms:
10 + 190 + 105t + -15t2 = -190 + 190

Combine like terms: 10 + 190 = 200
200 + 105t + -15t2 = -190 + 190

Combine like terms: -190 + 190 = 0
200 + 105t + -15t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(40 + 21t + -3t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(40 + 21t + -3t2)' equal to zero and attempt to solve:

Simplifying
40 + 21t + -3t2 = 0

Solving
40 + 21t + -3t2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-13.33333333 + -7t + t2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -7t + 13.33333333 + t2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -7t + t2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -7t + t2 = 0 + 13.33333333
-7t + t2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-7t + t2 = 13.33333333

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = 13.33333333 + 12.25

Reorder the terms:
12.25 + -7t + t2 = 13.33333333 + 12.25

Combine like terms: 13.33333333 + 12.25 = 25.58333333
12.25 + -7t + t2 = 25.58333333

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 25.58333333

Calculate the square root of the right side: 5.057996968

Break this problem into two subproblems by setting 
(t + -3.5) equal to 5.057996968 and -5.057996968.

Subproblem 1
t + -3.5 = 5.057996968

Simplifying
t + -3.5 = 5.057996968

Reorder the terms:
-3.5 + t = 5.057996968

Solving
-3.5 + t = 5.057996968

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 5.057996968 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 5.057996968 + 3.5
t = 5.057996968 + 3.5

Combine like terms: 5.057996968 + 3.5 = 8.557996968
t = 8.557996968

Simplifying
t = 8.557996968

Subproblem 2
t + -3.5 = -5.057996968

Simplifying
t + -3.5 = -5.057996968

Reorder the terms:
-3.5 + t = -5.057996968

Solving
-3.5 + t = -5.057996968

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -5.057996968 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -5.057996968 + 3.5
t = -5.057996968 + 3.5

Combine like terms: -5.057996968 + 3.5 = -1.557996968
t = -1.557996968

Simplifying
t = -1.557996968

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.557996968, -1.557996968}
Solution
t = {8.557996968, -1.557996968}