16t^2-76t+20=0

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Solution for 16t^2-76t+20=0 equation: 


Simplifying
16t2 + -76t + 20 = 0

Reorder the terms:
20 + -76t + 16t2 = 0

Solving
20 + -76t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -19t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -19t + 4t2)' equal to zero and attempt to solve:

Simplifying
5 + -19t + 4t2 = 0

Solving
5 + -19t + 4t2 = 0

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

Divide each side by '4'.
1.25 + -4.75t + t2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -4.75t + -1.25 + t2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -4.75t + t2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -4.75t + t2 = 0 + -1.25
-4.75t + t2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-4.75t + t2 = -1.25

The t term is -4.75t.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75t + 5.640625 + t2 = -1.25 + 5.640625

Reorder the terms:
5.640625 + -4.75t + t2 = -1.25 + 5.640625

Combine like terms: -1.25 + 5.640625 = 4.390625
5.640625 + -4.75t + t2 = 4.390625

Factor a perfect square on the left side:
(t + -2.375)(t + -2.375) = 4.390625

Calculate the square root of the right side: 2.095381827

Break this problem into two subproblems by setting 
(t + -2.375) equal to 2.095381827 and -2.095381827.


Subproblem 1
t + -2.375 = 2.095381827

Simplifying
t + -2.375 = 2.095381827

Reorder the terms:
-2.375 + t = 2.095381827

Solving
-2.375 + t = 2.095381827

Solving for variable 't'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + t = 2.095381827 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + t = 2.095381827 + 2.375
t = 2.095381827 + 2.375

Combine like terms: 2.095381827 + 2.375 = 4.470381827
t = 4.470381827

Simplifying
t = 4.470381827


Subproblem 2
t + -2.375 = -2.095381827

Simplifying
t + -2.375 = -2.095381827

Reorder the terms:
-2.375 + t = -2.095381827

Solving
-2.375 + t = -2.095381827

Solving for variable 't'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + t = -2.095381827 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + t = -2.095381827 + 2.375
t = -2.095381827 + 2.375

Combine like terms: -2.095381827 + 2.375 = 0.279618173
t = 0.279618173

Simplifying
t = 0.279618173


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.470381827, 0.279618173}
Solution
t = {4.470381827, 0.279618173}

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