0=-16t^2-30t+15

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Solution for 0=-16t^2-30t+15 equation: 


Simplifying
0 = -16t2 + -30t + 15

Reorder the terms:
0 = 15 + -30t + -16t2

Solving
0 = 15 + -30t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -15 = -15
-15 + 30t + 16t2 = 15 + -30t + -16t2 + -15 + 30t + 16t2

Reorder the terms:
-15 + 30t + 16t2 = 15 + -15 + -30t + 30t + -16t2 + 16t2

Combine like terms: 15 + -15 = 0
-15 + 30t + 16t2 = 0 + -30t + 30t + -16t2 + 16t2
-15 + 30t + 16t2 = -30t + 30t + -16t2 + 16t2

Combine like terms: -30t + 30t = 0
-15 + 30t + 16t2 = 0 + -16t2 + 16t2
-15 + 30t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-15 + 30t + 16t2 = 0

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

Divide each side by '16'.
-0.9375 + 1.875t + t2 = 0

Move the constant term to the right:

Add '0.9375' to each side of the equation.
-0.9375 + 1.875t + 0.9375 + t2 = 0 + 0.9375

Reorder the terms:
-0.9375 + 0.9375 + 1.875t + t2 = 0 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + 1.875t + t2 = 0 + 0.9375
1.875t + t2 = 0 + 0.9375

Combine like terms: 0 + 0.9375 = 0.9375
1.875t + t2 = 0.9375

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 = 0.9375 + 0.87890625

Reorder the terms:
0.87890625 + 1.875t + t2 = 0.9375 + 0.87890625

Combine like terms: 0.9375 + 0.87890625 = 1.81640625
0.87890625 + 1.875t + t2 = 1.81640625

Factor a perfect square on the left side:
(t + 0.9375)(t + 0.9375) = 1.81640625

Calculate the square root of the right side: 1.347741166

Break this problem into two subproblems by setting 
(t + 0.9375) equal to 1.347741166 and -1.347741166.


Subproblem 1
t + 0.9375 = 1.347741166

Simplifying
t + 0.9375 = 1.347741166

Reorder the terms:
0.9375 + t = 1.347741166

Solving
0.9375 + t = 1.347741166

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 = 1.347741166 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + t = 1.347741166 + -0.9375
t = 1.347741166 + -0.9375

Combine like terms: 1.347741166 + -0.9375 = 0.410241166
t = 0.410241166

Simplifying
t = 0.410241166


Subproblem 2
t + 0.9375 = -1.347741166

Simplifying
t + 0.9375 = -1.347741166

Reorder the terms:
0.9375 + t = -1.347741166

Solving
0.9375 + t = -1.347741166

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 = -1.347741166 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + t = -1.347741166 + -0.9375
t = -1.347741166 + -0.9375

Combine like terms: -1.347741166 + -0.9375 = -2.285241166
t = -2.285241166

Simplifying
t = -2.285241166


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.410241166, -2.285241166}

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