16t^2+30t-500=0

Solution for 16t^2+30t-500=0 equation:

Simplifying
16t2 + 30t + -500 = 0

Reorder the terms:
-500 + 30t + 16t2 = 0

Solving
-500 + 30t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-250 + 15t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-250 + 15t + 8t2)' equal to zero and attempt to solve:

Simplifying
-250 + 15t + 8t2 = 0

Solving
-250 + 15t + 8t2 = 0

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

Divide each side by '8'.
-31.25 + 1.875t + t2 = 0

Move the constant term to the right:

Add '31.25' to each side of the equation.
-31.25 + 1.875t + 31.25 + t2 = 0 + 31.25

Reorder the terms:
-31.25 + 31.25 + 1.875t + t2 = 0 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + 1.875t + t2 = 0 + 31.25
1.875t + t2 = 0 + 31.25

Combine like terms: 0 + 31.25 = 31.25
1.875t + t2 = 31.25

The t term is 1.875t.  Take half its coefficient (0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
1.875t + 0.87890625 + t2 = 31.25 + 0.87890625

Reorder the terms:
0.87890625 + 1.875t + t2 = 31.25 + 0.87890625

Combine like terms: 31.25 + 0.87890625 = 32.12890625
0.87890625 + 1.875t + t2 = 32.12890625

Factor a perfect square on the left side:
(t + 0.9375)(t + 0.9375) = 32.12890625

Calculate the square root of the right side: 5.668236609

Break this problem into two subproblems by setting 
(t + 0.9375) equal to 5.668236609 and -5.668236609.

Subproblem 1
t + 0.9375 = 5.668236609

Simplifying
t + 0.9375 = 5.668236609

Reorder the terms:
0.9375 + t = 5.668236609

Solving
0.9375 + t = 5.668236609

Solving for variable 't'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + t = 5.668236609 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + t = 5.668236609 + -0.9375
t = 5.668236609 + -0.9375

Combine like terms: 5.668236609 + -0.9375 = 4.730736609
t = 4.730736609

Simplifying
t = 4.730736609

Subproblem 2
t + 0.9375 = -5.668236609

Simplifying
t + 0.9375 = -5.668236609

Reorder the terms:
0.9375 + t = -5.668236609

Solving
0.9375 + t = -5.668236609

Solving for variable 't'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + t = -5.668236609 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + t = -5.668236609 + -0.9375
t = -5.668236609 + -0.9375

Combine like terms: -5.668236609 + -0.9375 = -6.605736609
t = -6.605736609

Simplifying
t = -6.605736609

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.730736609, -6.605736609}
Solution
t = {4.730736609, -6.605736609}