0=16t^2+47t+3

Solution for 0=16t^2+47t+3 equation:

Simplifying
0 = 16t2 + 47t + 3

Reorder the terms:
0 = 3 + 47t + 16t2

Solving
0 = 3 + 47t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -3 = -3
-3 + -47t + -16t2 = 3 + 47t + 16t2 + -3 + -47t + -16t2

Reorder the terms:
-3 + -47t + -16t2 = 3 + -3 + 47t + -47t + 16t2 + -16t2

Combine like terms: 3 + -3 = 0
-3 + -47t + -16t2 = 0 + 47t + -47t + 16t2 + -16t2
-3 + -47t + -16t2 = 47t + -47t + 16t2 + -16t2

Combine like terms: 47t + -47t = 0
-3 + -47t + -16t2 = 0 + 16t2 + -16t2
-3 + -47t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-3 + -47t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 47t + 16t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 47t + 16t2)' equal to zero and attempt to solve:

Simplifying
3 + 47t + 16t2 = 0

Solving
3 + 47t + 16t2 = 0

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

Divide each side by '16'.
0.1875 + 2.9375t + t2 = 0

Move the constant term to the right:

Add '-0.1875' to each side of the equation.
0.1875 + 2.9375t + -0.1875 + t2 = 0 + -0.1875

Reorder the terms:
0.1875 + -0.1875 + 2.9375t + t2 = 0 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + 2.9375t + t2 = 0 + -0.1875
2.9375t + t2 = 0 + -0.1875

Combine like terms: 0 + -0.1875 = -0.1875
2.9375t + t2 = -0.1875

The t term is 2.9375t.  Take half its coefficient (1.46875).
Square it (2.157226563) and add it to both sides.

Add '2.157226563' to each side of the equation.
2.9375t + 2.157226563 + t2 = -0.1875 + 2.157226563

Reorder the terms:
2.157226563 + 2.9375t + t2 = -0.1875 + 2.157226563

Combine like terms: -0.1875 + 2.157226563 = 1.969726563
2.157226563 + 2.9375t + t2 = 1.969726563

Factor a perfect square on the left side:
(t + 1.46875)(t + 1.46875) = 1.969726563

Calculate the square root of the right side: 1.403469473

Break this problem into two subproblems by setting 
(t + 1.46875) equal to 1.403469473 and -1.403469473.

Subproblem 1
t + 1.46875 = 1.403469473

Simplifying
t + 1.46875 = 1.403469473

Reorder the terms:
1.46875 + t = 1.403469473

Solving
1.46875 + t = 1.403469473

Solving for variable 't'.

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

Add '-1.46875' to each side of the equation.
1.46875 + -1.46875 + t = 1.403469473 + -1.46875

Combine like terms: 1.46875 + -1.46875 = 0.00000
0.00000 + t = 1.403469473 + -1.46875
t = 1.403469473 + -1.46875

Combine like terms: 1.403469473 + -1.46875 = -0.065280527
t = -0.065280527

Simplifying
t = -0.065280527

Subproblem 2
t + 1.46875 = -1.403469473

Simplifying
t + 1.46875 = -1.403469473

Reorder the terms:
1.46875 + t = -1.403469473

Solving
1.46875 + t = -1.403469473

Solving for variable 't'.

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

Add '-1.46875' to each side of the equation.
1.46875 + -1.46875 + t = -1.403469473 + -1.46875

Combine like terms: 1.46875 + -1.46875 = 0.00000
0.00000 + t = -1.403469473 + -1.46875
t = -1.403469473 + -1.46875

Combine like terms: -1.403469473 + -1.46875 = -2.872219473
t = -2.872219473

Simplifying
t = -2.872219473

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.065280527, -2.872219473}
Solution
t = {-0.065280527, -2.872219473}