0=16t^2+40t+7

Solution for 0=16t^2+40t+7 equation:

Simplifying
0 = 16t2 + 40t + 7

Reorder the terms:
0 = 7 + 40t + 16t2

Solving
0 = 7 + 40t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -7 = -7
-7 + -40t + -16t2 = 7 + 40t + 16t2 + -7 + -40t + -16t2

Reorder the terms:
-7 + -40t + -16t2 = 7 + -7 + 40t + -40t + 16t2 + -16t2

Combine like terms: 7 + -7 = 0
-7 + -40t + -16t2 = 0 + 40t + -40t + 16t2 + -16t2
-7 + -40t + -16t2 = 40t + -40t + 16t2 + -16t2

Combine like terms: 40t + -40t = 0
-7 + -40t + -16t2 = 0 + 16t2 + -16t2
-7 + -40t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-7 + -40t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 40t + 16t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 40t + 16t2)' equal to zero and attempt to solve:

Simplifying
7 + 40t + 16t2 = 0

Solving
7 + 40t + 16t2 = 0

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

Divide each side by '16'.
0.4375 + 2.5t + t2 = 0

Move the constant term to the right:

Add '-0.4375' to each side of the equation.
0.4375 + 2.5t + -0.4375 + t2 = 0 + -0.4375

Reorder the terms:
0.4375 + -0.4375 + 2.5t + t2 = 0 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + 2.5t + t2 = 0 + -0.4375
2.5t + t2 = 0 + -0.4375

Combine like terms: 0 + -0.4375 = -0.4375
2.5t + t2 = -0.4375

The t term is 2.5t.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5t + 1.5625 + t2 = -0.4375 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = -0.4375 + 1.5625

Combine like terms: -0.4375 + 1.5625 = 1.125
1.5625 + 2.5t + t2 = 1.125

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 1.125

Calculate the square root of the right side: 1.060660172

Break this problem into two subproblems by setting 
(t + 1.25) equal to 1.060660172 and -1.060660172.

Subproblem 1
t + 1.25 = 1.060660172

Simplifying
t + 1.25 = 1.060660172

Reorder the terms:
1.25 + t = 1.060660172

Solving
1.25 + t = 1.060660172

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = 1.060660172 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = 1.060660172 + -1.25
t = 1.060660172 + -1.25

Combine like terms: 1.060660172 + -1.25 = -0.189339828
t = -0.189339828

Simplifying
t = -0.189339828

Subproblem 2
t + 1.25 = -1.060660172

Simplifying
t + 1.25 = -1.060660172

Reorder the terms:
1.25 + t = -1.060660172

Solving
1.25 + t = -1.060660172

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = -1.060660172 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = -1.060660172 + -1.25
t = -1.060660172 + -1.25

Combine like terms: -1.060660172 + -1.25 = -2.310660172
t = -2.310660172

Simplifying
t = -2.310660172

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.189339828, -2.310660172}
Solution
t = {-0.189339828, -2.310660172}