0=-16t^2+32t+30

Solution for 0=-16t^2+32t+30 equation:

Simplifying
0 = -16t2 + 32t + 30

Reorder the terms:
0 = 30 + 32t + -16t2

Solving
0 = 30 + 32t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -30 = -30
-30 + -32t + 16t2 = 30 + 32t + -16t2 + -30 + -32t + 16t2

Reorder the terms:
-30 + -32t + 16t2 = 30 + -30 + 32t + -32t + -16t2 + 16t2

Combine like terms: 30 + -30 = 0
-30 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2
-30 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-30 + -32t + 16t2 = 0 + -16t2 + 16t2
-30 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-30 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -16t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + -16t + 8t2)' equal to zero and attempt to solve:

Simplifying
-15 + -16t + 8t2 = 0

Solving
-15 + -16t + 8t2 = 0

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

Divide each side by '8'.
-1.875 + -2t + t2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -2t + 1.875 + t2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -2t + t2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -2t + t2 = 0 + 1.875
-2t + t2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-2t + t2 = 1.875

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 = 1.875 + 1

Reorder the terms:
1 + -2t + t2 = 1.875 + 1

Combine like terms: 1.875 + 1 = 2.875
1 + -2t + t2 = 2.875

Factor a perfect square on the left side:
(t + -1)(t + -1) = 2.875

Calculate the square root of the right side: 1.695582496

Break this problem into two subproblems by setting 
(t + -1) equal to 1.695582496 and -1.695582496.

Subproblem 1
t + -1 = 1.695582496

Simplifying
t + -1 = 1.695582496

Reorder the terms:
-1 + t = 1.695582496

Solving
-1 + t = 1.695582496

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 = 1.695582496 + 1

Combine like terms: -1 + 1 = 0
0 + t = 1.695582496 + 1
t = 1.695582496 + 1

Combine like terms: 1.695582496 + 1 = 2.695582496
t = 2.695582496

Simplifying
t = 2.695582496

Subproblem 2
t + -1 = -1.695582496

Simplifying
t + -1 = -1.695582496

Reorder the terms:
-1 + t = -1.695582496

Solving
-1 + t = -1.695582496

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 = -1.695582496 + 1

Combine like terms: -1 + 1 = 0
0 + t = -1.695582496 + 1
t = -1.695582496 + 1

Combine like terms: -1.695582496 + 1 = -0.695582496
t = -0.695582496

Simplifying
t = -0.695582496

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.695582496, -0.695582496}
Solution
t = {2.695582496, -0.695582496}