16t^2-27t+10=0

Solution for 16t^2-27t+10=0 equation:

Simplifying
16t2 + -27t + 10 = 0

Reorder the terms:
10 + -27t + 16t2 = 0

Solving
10 + -27t + 16t2 = 0

Solving for variable 't'.

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

Divide each side by '16'.
0.625 + -1.6875t + t2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -1.6875t + -0.625 + t2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -1.6875t + t2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -1.6875t + t2 = 0 + -0.625
-1.6875t + t2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-1.6875t + t2 = -0.625

The t term is -1.6875t.  Take half its coefficient (-0.84375).
Square it (0.7119140625) and add it to both sides.

Add '0.7119140625' to each side of the equation.
-1.6875t + 0.7119140625 + t2 = -0.625 + 0.7119140625

Reorder the terms:
0.7119140625 + -1.6875t + t2 = -0.625 + 0.7119140625

Combine like terms: -0.625 + 0.7119140625 = 0.0869140625
0.7119140625 + -1.6875t + t2 = 0.0869140625

Factor a perfect square on the left side:
(t + -0.84375)(t + -0.84375) = 0.0869140625

Calculate the square root of the right side: 0.29481191

Break this problem into two subproblems by setting 
(t + -0.84375) equal to 0.29481191 and -0.29481191.

Subproblem 1
t + -0.84375 = 0.29481191

Simplifying
t + -0.84375 = 0.29481191

Reorder the terms:
-0.84375 + t = 0.29481191

Solving
-0.84375 + t = 0.29481191

Solving for variable 't'.

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

Add '0.84375' to each side of the equation.
-0.84375 + 0.84375 + t = 0.29481191 + 0.84375

Combine like terms: -0.84375 + 0.84375 = 0.00000
0.00000 + t = 0.29481191 + 0.84375
t = 0.29481191 + 0.84375

Combine like terms: 0.29481191 + 0.84375 = 1.13856191
t = 1.13856191

Simplifying
t = 1.13856191

Subproblem 2
t + -0.84375 = -0.29481191

Simplifying
t + -0.84375 = -0.29481191

Reorder the terms:
-0.84375 + t = -0.29481191

Solving
-0.84375 + t = -0.29481191

Solving for variable 't'.

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

Add '0.84375' to each side of the equation.
-0.84375 + 0.84375 + t = -0.29481191 + 0.84375

Combine like terms: -0.84375 + 0.84375 = 0.00000
0.00000 + t = -0.29481191 + 0.84375
t = -0.29481191 + 0.84375

Combine like terms: -0.29481191 + 0.84375 = 0.54893809
t = 0.54893809

Simplifying
t = 0.54893809

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.13856191, 0.54893809}