-5t^2-22t-15=0

Solution for -5t^2-22t-15=0 equation:

Simplifying
-5t2 + -22t + -15 = 0

Reorder the terms:
-15 + -22t + -5t2 = 0

Solving
-15 + -22t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 22t + 5t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(15 + 22t + 5t2)' equal to zero and attempt to solve:

Simplifying
15 + 22t + 5t2 = 0

Solving
15 + 22t + 5t2 = 0

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

Divide each side by '5'.
3 + 4.4t + t2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 4.4t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + 4.4t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4.4t + t2 = 0 + -3
4.4t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
4.4t + t2 = -3

The t term is 4.4t.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4t + 4.84 + t2 = -3 + 4.84

Reorder the terms:
4.84 + 4.4t + t2 = -3 + 4.84

Combine like terms: -3 + 4.84 = 1.84
4.84 + 4.4t + t2 = 1.84

Factor a perfect square on the left side:
(t + 2.2)(t + 2.2) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(t + 2.2) equal to 1.356465997 and -1.356465997.

Subproblem 1
t + 2.2 = 1.356465997

Simplifying
t + 2.2 = 1.356465997

Reorder the terms:
2.2 + t = 1.356465997

Solving
2.2 + t = 1.356465997

Solving for variable 't'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + t = 1.356465997 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + t = 1.356465997 + -2.2
t = 1.356465997 + -2.2

Combine like terms: 1.356465997 + -2.2 = -0.843534003
t = -0.843534003

Simplifying
t = -0.843534003

Subproblem 2
t + 2.2 = -1.356465997

Simplifying
t + 2.2 = -1.356465997

Reorder the terms:
2.2 + t = -1.356465997

Solving
2.2 + t = -1.356465997

Solving for variable 't'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + t = -1.356465997 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + t = -1.356465997 + -2.2
t = -1.356465997 + -2.2

Combine like terms: -1.356465997 + -2.2 = -3.556465997
t = -3.556465997

Simplifying
t = -3.556465997

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.843534003, -3.556465997}
Solution
t = {-0.843534003, -3.556465997}