-16t^2+112t+20=0

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Solution for -16t^2+112t+20=0 equation: 


Simplifying
-16t2 + 112t + 20 = 0

Reorder the terms:
20 + 112t + -16t2 = 0

Solving
20 + 112t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 28t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + 28t + -4t2)' equal to zero and attempt to solve:

Simplifying
5 + 28t + -4t2 = 0

Solving
5 + 28t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.25 + -7t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -7t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -7t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -7t + t2 = 0 + 1.25
-7t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-7t + t2 = 1.25

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = 1.25 + 12.25

Reorder the terms:
12.25 + -7t + t2 = 1.25 + 12.25

Combine like terms: 1.25 + 12.25 = 13.5
12.25 + -7t + t2 = 13.5

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 13.5

Calculate the square root of the right side: 3.674234614

Break this problem into two subproblems by setting 
(t + -3.5) equal to 3.674234614 and -3.674234614.


Subproblem 1
t + -3.5 = 3.674234614

Simplifying
t + -3.5 = 3.674234614

Reorder the terms:
-3.5 + t = 3.674234614

Solving
-3.5 + t = 3.674234614

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 3.674234614 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 3.674234614 + 3.5
t = 3.674234614 + 3.5

Combine like terms: 3.674234614 + 3.5 = 7.174234614
t = 7.174234614

Simplifying
t = 7.174234614


Subproblem 2
t + -3.5 = -3.674234614

Simplifying
t + -3.5 = -3.674234614

Reorder the terms:
-3.5 + t = -3.674234614

Solving
-3.5 + t = -3.674234614

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -3.674234614 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -3.674234614 + 3.5
t = -3.674234614 + 3.5

Combine like terms: -3.674234614 + 3.5 = -0.174234614
t = -0.174234614

Simplifying
t = -0.174234614


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.174234614, -0.174234614}
Solution
t = {7.174234614, -0.174234614}

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