16y(y-4)+6y=20y-1(50)

Solution for 16y(y-4)+6y=20y-1(50) equation:

Simplifying
16y(y + -4) + 6y = 20y + -1(50)

Reorder the terms:
16y(-4 + y) + 6y = 20y + -1(50)
(-4 * 16y + y * 16y) + 6y = 20y + -1(50)
(-64y + 16y2) + 6y = 20y + -1(50)

Reorder the terms:
-64y + 6y + 16y2 = 20y + -1(50)

Combine like terms: -64y + 6y = -58y
-58y + 16y2 = 20y + -1(50)

Multiply -1 * 50
-58y + 16y2 = 20y + -50

Reorder the terms:
-58y + 16y2 = -50 + 20y

Solving
-58y + 16y2 = -50 + 20y

Solving for variable 'y'.

Reorder the terms:
50 + -58y + -20y + 16y2 = -50 + 20y + 50 + -20y

Combine like terms: -58y + -20y = -78y
50 + -78y + 16y2 = -50 + 20y + 50 + -20y

Reorder the terms:
50 + -78y + 16y2 = -50 + 50 + 20y + -20y

Combine like terms: -50 + 50 = 0
50 + -78y + 16y2 = 0 + 20y + -20y
50 + -78y + 16y2 = 20y + -20y

Combine like terms: 20y + -20y = 0
50 + -78y + 16y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -39y + 8y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(25 + -39y + 8y2)' equal to zero and attempt to solve:

Simplifying
25 + -39y + 8y2 = 0

Solving
25 + -39y + 8y2 = 0

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

Divide each side by '8'.
3.125 + -4.875y + y2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + -4.875y + -3.125 + y2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + -4.875y + y2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + -4.875y + y2 = 0 + -3.125
-4.875y + y2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
-4.875y + y2 = -3.125

The y term is -4.875y.  Take half its coefficient (-2.4375).
Square it (5.94140625) and add it to both sides.

Add '5.94140625' to each side of the equation.
-4.875y + 5.94140625 + y2 = -3.125 + 5.94140625

Reorder the terms:
5.94140625 + -4.875y + y2 = -3.125 + 5.94140625

Combine like terms: -3.125 + 5.94140625 = 2.81640625
5.94140625 + -4.875y + y2 = 2.81640625

Factor a perfect square on the left side:
(y + -2.4375)(y + -2.4375) = 2.81640625

Calculate the square root of the right side: 1.678215198

Break this problem into two subproblems by setting 
(y + -2.4375) equal to 1.678215198 and -1.678215198.

Subproblem 1
y + -2.4375 = 1.678215198

Simplifying
y + -2.4375 = 1.678215198

Reorder the terms:
-2.4375 + y = 1.678215198

Solving
-2.4375 + y = 1.678215198

Solving for variable 'y'.

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

Add '2.4375' to each side of the equation.
-2.4375 + 2.4375 + y = 1.678215198 + 2.4375

Combine like terms: -2.4375 + 2.4375 = 0.0000
0.0000 + y = 1.678215198 + 2.4375
y = 1.678215198 + 2.4375

Combine like terms: 1.678215198 + 2.4375 = 4.115715198
y = 4.115715198

Simplifying
y = 4.115715198

Subproblem 2
y + -2.4375 = -1.678215198

Simplifying
y + -2.4375 = -1.678215198

Reorder the terms:
-2.4375 + y = -1.678215198

Solving
-2.4375 + y = -1.678215198

Solving for variable 'y'.

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

Add '2.4375' to each side of the equation.
-2.4375 + 2.4375 + y = -1.678215198 + 2.4375

Combine like terms: -2.4375 + 2.4375 = 0.0000
0.0000 + y = -1.678215198 + 2.4375
y = -1.678215198 + 2.4375

Combine like terms: -1.678215198 + 2.4375 = 0.759284802
y = 0.759284802

Simplifying
y = 0.759284802

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.115715198, 0.759284802}
Solution
y = {4.115715198, 0.759284802}