0=16t^2+25t+3

Solution for 0=16t^2+25t+3 equation:

Simplifying
0 = 16t2 + 25t + 3

Reorder the terms:
0 = 3 + 25t + 16t2

Solving
0 = 3 + 25t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -3 = -3
-3 + -25t + -16t2 = 3 + 25t + 16t2 + -3 + -25t + -16t2

Reorder the terms:
-3 + -25t + -16t2 = 3 + -3 + 25t + -25t + 16t2 + -16t2

Combine like terms: 3 + -3 = 0
-3 + -25t + -16t2 = 0 + 25t + -25t + 16t2 + -16t2
-3 + -25t + -16t2 = 25t + -25t + 16t2 + -16t2

Combine like terms: 25t + -25t = 0
-3 + -25t + -16t2 = 0 + 16t2 + -16t2
-3 + -25t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-3 + -25t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 25t + 16t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 25t + 16t2)' equal to zero and attempt to solve:

Simplifying
3 + 25t + 16t2 = 0

Solving
3 + 25t + 16t2 = 0

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

Divide each side by '16'.
0.1875 + 1.5625t + t2 = 0

Move the constant term to the right:

Add '-0.1875' to each side of the equation.
0.1875 + 1.5625t + -0.1875 + t2 = 0 + -0.1875

Reorder the terms:
0.1875 + -0.1875 + 1.5625t + t2 = 0 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + 1.5625t + t2 = 0 + -0.1875
1.5625t + t2 = 0 + -0.1875

Combine like terms: 0 + -0.1875 = -0.1875
1.5625t + t2 = -0.1875

The t term is 1.5625t.  Take half its coefficient (0.78125).
Square it (0.6103515625) and add it to both sides.

Add '0.6103515625' to each side of the equation.
1.5625t + 0.6103515625 + t2 = -0.1875 + 0.6103515625

Reorder the terms:
0.6103515625 + 1.5625t + t2 = -0.1875 + 0.6103515625

Combine like terms: -0.1875 + 0.6103515625 = 0.4228515625
0.6103515625 + 1.5625t + t2 = 0.4228515625

Factor a perfect square on the left side:
(t + 0.78125)(t + 0.78125) = 0.4228515625

Calculate the square root of the right side: 0.650270376

Break this problem into two subproblems by setting 
(t + 0.78125) equal to 0.650270376 and -0.650270376.

Subproblem 1
t + 0.78125 = 0.650270376

Simplifying
t + 0.78125 = 0.650270376

Reorder the terms:
0.78125 + t = 0.650270376

Solving
0.78125 + t = 0.650270376

Solving for variable 't'.

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

Add '-0.78125' to each side of the equation.
0.78125 + -0.78125 + t = 0.650270376 + -0.78125

Combine like terms: 0.78125 + -0.78125 = 0.00000
0.00000 + t = 0.650270376 + -0.78125
t = 0.650270376 + -0.78125

Combine like terms: 0.650270376 + -0.78125 = -0.130979624
t = -0.130979624

Simplifying
t = -0.130979624

Subproblem 2
t + 0.78125 = -0.650270376

Simplifying
t + 0.78125 = -0.650270376

Reorder the terms:
0.78125 + t = -0.650270376

Solving
0.78125 + t = -0.650270376

Solving for variable 't'.

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

Add '-0.78125' to each side of the equation.
0.78125 + -0.78125 + t = -0.650270376 + -0.78125

Combine like terms: 0.78125 + -0.78125 = 0.00000
0.00000 + t = -0.650270376 + -0.78125
t = -0.650270376 + -0.78125

Combine like terms: -0.650270376 + -0.78125 = -1.431520376
t = -1.431520376

Simplifying
t = -1.431520376

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.130979624, -1.431520376}
Solution
t = {-0.130979624, -1.431520376}