-16t^2+126t+72=0

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Solution for -16t^2+126t+72=0 equation: 


Simplifying
-16t2 + 126t + 72 = 0

Reorder the terms:
72 + 126t + -16t2 = 0

Solving
72 + 126t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + 63t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(36 + 63t + -8t2)' equal to zero and attempt to solve:

Simplifying
36 + 63t + -8t2 = 0

Solving
36 + 63t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-4.5 + -7.875t + t2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -7.875t + 4.5 + t2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -7.875t + t2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -7.875t + t2 = 0 + 4.5
-7.875t + t2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-7.875t + t2 = 4.5

The t term is -7.875t.  Take half its coefficient (-3.9375).
Square it (15.50390625) and add it to both sides.

Add '15.50390625' to each side of the equation.
-7.875t + 15.50390625 + t2 = 4.5 + 15.50390625

Reorder the terms:
15.50390625 + -7.875t + t2 = 4.5 + 15.50390625

Combine like terms: 4.5 + 15.50390625 = 20.00390625
15.50390625 + -7.875t + t2 = 20.00390625

Factor a perfect square on the left side:
(t + -3.9375)(t + -3.9375) = 20.00390625

Calculate the square root of the right side: 4.472572666

Break this problem into two subproblems by setting 
(t + -3.9375) equal to 4.472572666 and -4.472572666.


Subproblem 1
t + -3.9375 = 4.472572666

Simplifying
t + -3.9375 = 4.472572666

Reorder the terms:
-3.9375 + t = 4.472572666

Solving
-3.9375 + t = 4.472572666

Solving for variable 't'.

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

Add '3.9375' to each side of the equation.
-3.9375 + 3.9375 + t = 4.472572666 + 3.9375

Combine like terms: -3.9375 + 3.9375 = 0.0000
0.0000 + t = 4.472572666 + 3.9375
t = 4.472572666 + 3.9375

Combine like terms: 4.472572666 + 3.9375 = 8.410072666
t = 8.410072666

Simplifying
t = 8.410072666


Subproblem 2
t + -3.9375 = -4.472572666

Simplifying
t + -3.9375 = -4.472572666

Reorder the terms:
-3.9375 + t = -4.472572666

Solving
-3.9375 + t = -4.472572666

Solving for variable 't'.

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

Add '3.9375' to each side of the equation.
-3.9375 + 3.9375 + t = -4.472572666 + 3.9375

Combine like terms: -3.9375 + 3.9375 = 0.0000
0.0000 + t = -4.472572666 + 3.9375
t = -4.472572666 + 3.9375

Combine like terms: -4.472572666 + 3.9375 = -0.535072666
t = -0.535072666

Simplifying
t = -0.535072666


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.410072666, -0.535072666}
Solution
t = {8.410072666, -0.535072666}

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