-16(t^2-1.5t+0.5625)=-15

Solution for -16(t^2-1.5t+0.5625)=-15 equation:

Simplifying
-16(t2 + -1.5t + 0.5625) = -15

Reorder the terms:
-16(0.5625 + -1.5t + t2) = -15
(0.5625 * -16 + -1.5t * -16 + t2 * -16) = -15
(-9 + 24t + -16t2) = -15

Solving
-9 + 24t + -16t2 = -15

Solving for variable 't'.

Reorder the terms:
-9 + 15 + 24t + -16t2 = -15 + 15

Combine like terms: -9 + 15 = 6
6 + 24t + -16t2 = -15 + 15

Combine like terms: -15 + 15 = 0
6 + 24t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 12t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 12t + -8t2)' equal to zero and attempt to solve:

Simplifying
3 + 12t + -8t2 = 0

Solving
3 + 12t + -8t2 = 0

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

Divide each side by '-8'.
-0.375 + -1.5t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -1.5t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -1.5t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -1.5t + t2 = 0 + 0.375
-1.5t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-1.5t + t2 = 0.375

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = 0.375 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = 0.375 + 0.5625

Combine like terms: 0.375 + 0.5625 = 0.9375
0.5625 + -1.5t + t2 = 0.9375

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 0.9375

Calculate the square root of the right side: 0.968245837

Break this problem into two subproblems by setting 
(t + -0.75) equal to 0.968245837 and -0.968245837.

Subproblem 1
t + -0.75 = 0.968245837

Simplifying
t + -0.75 = 0.968245837

Reorder the terms:
-0.75 + t = 0.968245837

Solving
-0.75 + t = 0.968245837

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = 0.968245837 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = 0.968245837 + 0.75
t = 0.968245837 + 0.75

Combine like terms: 0.968245837 + 0.75 = 1.718245837
t = 1.718245837

Simplifying
t = 1.718245837

Subproblem 2
t + -0.75 = -0.968245837

Simplifying
t + -0.75 = -0.968245837

Reorder the terms:
-0.75 + t = -0.968245837

Solving
-0.75 + t = -0.968245837

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = -0.968245837 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = -0.968245837 + 0.75
t = -0.968245837 + 0.75

Combine like terms: -0.968245837 + 0.75 = -0.218245837
t = -0.218245837

Simplifying
t = -0.218245837

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.718245837, -0.218245837}
Solution
t = {1.718245837, -0.218245837}