0=(-16t^2)-(18t)+30

Solution for 0=(-16t^2)-(18t)+30 equation:

Simplifying
0 = (-16t2) + -1(18t) + 30

Remove parenthesis around (18t)
0 = (-16t2) + -1 * 18t + 30

Multiply -1 * 18
0 = (-16t2) + -18t + 30

Reorder the terms:
0 = 30 + -18t + (-16t2)

Solving
0 = 30 + -18t + (-16t2)

Solving for variable 't'.

Combine like terms: 0 + -30 = -30
-30 + 18t + (16t2) = 30 + -18t + (-16t2) + -30 + 18t + (16t2)

Reorder the terms:
-30 + 18t + (16t2) = 30 + -30 + -18t + 18t + (-16t2) + (16t2)

Combine like terms: 30 + -30 = 0
-30 + 18t + (16t2) = 0 + -18t + 18t + (-16t2) + (16t2)
-30 + 18t + (16t2) = -18t + 18t + (-16t2) + (16t2)

Combine like terms: -18t + 18t = 0
-30 + 18t + (16t2) = 0 + (-16t2) + (16t2)
-30 + 18t + (16t2) = (-16t2) + (16t2)

Combine like terms: (-16t2) + (16t2) = 0
-30 + 18t + (16t2) = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 9t + (8t2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + 9t + (8t2))' equal to zero and attempt to solve:

Simplifying
-15 + 9t + (8t2) = 0

Solving
-15 + 9t + (8t2) = 0

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

Divide each side by '8'.
-1.875 + 1.125t + t2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 1.125t + 1.875 + t2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 1.125t + t2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 1.125t + t2 = 0 + 1.875
1.125t + t2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
1.125t + t2 = 1.875

The t term is 1.125t.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125t + 0.31640625 + t2 = 1.875 + 0.31640625

Reorder the terms:
0.31640625 + 1.125t + t2 = 1.875 + 0.31640625

Combine like terms: 1.875 + 0.31640625 = 2.19140625
0.31640625 + 1.125t + t2 = 2.19140625

Factor a perfect square on the left side:
((t) + 0.5625)((t) + 0.5625) = 2.19140625

Calculate the square root of the right side: 1.48033991

Break this problem into two subproblems by setting 
((t) + 0.5625) equal to 1.48033991 and -1.48033991.

Subproblem 1
(t) + 0.5625 = 1.48033991

Simplifying
(t) + 0.5625 = 1.48033991
t + 0.5625 = 1.48033991

Reorder the terms:
0.5625 + t = 1.48033991

Solving
0.5625 + t = 1.48033991

Solving for variable 't'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + t = 1.48033991 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + t = 1.48033991 + -0.5625
t = 1.48033991 + -0.5625

Combine like terms: 1.48033991 + -0.5625 = 0.91783991
t = 0.91783991

Simplifying
t = 0.91783991

Subproblem 2
(t) + 0.5625 = -1.48033991

Simplifying
(t) + 0.5625 = -1.48033991
t + 0.5625 = -1.48033991

Reorder the terms:
0.5625 + t = -1.48033991

Solving
0.5625 + t = -1.48033991

Solving for variable 't'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + t = -1.48033991 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + t = -1.48033991 + -0.5625
t = -1.48033991 + -0.5625

Combine like terms: -1.48033991 + -0.5625 = -2.04283991
t = -2.04283991

Simplifying
t = -2.04283991

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.91783991, -2.04283991}
Solution
t = {0.91783991, -2.04283991}