16t^2+64t+40=0

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Solution for 16t^2+64t+40=0 equation: 


Simplifying
16t2 + 64t + 40 = 0

Reorder the terms:
40 + 64t + 16t2 = 0

Solving
40 + 64t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + 8t + 2t2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(5 + 8t + 2t2)' equal to zero and attempt to solve:

Simplifying
5 + 8t + 2t2 = 0

Solving
5 + 8t + 2t2 = 0

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

Divide each side by '2'.
2.5 + 4t + t2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 4t + -2.5 + t2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 4t + t2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 4t + t2 = 0 + -2.5
4t + t2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
4t + t2 = -2.5

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = -2.5 + 4

Reorder the terms:
4 + 4t + t2 = -2.5 + 4

Combine like terms: -2.5 + 4 = 1.5
4 + 4t + t2 = 1.5

Factor a perfect square on the left side:
(t + 2)(t + 2) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(t + 2) equal to 1.224744871 and -1.224744871.


Subproblem 1
t + 2 = 1.224744871

Simplifying
t + 2 = 1.224744871

Reorder the terms:
2 + t = 1.224744871

Solving
2 + t = 1.224744871

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 1.224744871 + -2

Combine like terms: 2 + -2 = 0
0 + t = 1.224744871 + -2
t = 1.224744871 + -2

Combine like terms: 1.224744871 + -2 = -0.775255129
t = -0.775255129

Simplifying
t = -0.775255129


Subproblem 2
t + 2 = -1.224744871

Simplifying
t + 2 = -1.224744871

Reorder the terms:
2 + t = -1.224744871

Solving
2 + t = -1.224744871

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -1.224744871 + -2

Combine like terms: 2 + -2 = 0
0 + t = -1.224744871 + -2
t = -1.224744871 + -2

Combine like terms: -1.224744871 + -2 = -3.224744871
t = -3.224744871

Simplifying
t = -3.224744871


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.775255129, -3.224744871}
Solution
t = {-0.775255129, -3.224744871}

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