-5y(2y-9)-y=2(y-4)

Solution for -5y(2y-9)-y=2(y-4) equation:

Simplifying
-5y(2y + -9) + -1y = 2(y + -4)

Reorder the terms:
-5y(-9 + 2y) + -1y = 2(y + -4)
(-9 * -5y + 2y * -5y) + -1y = 2(y + -4)
(45y + -10y2) + -1y = 2(y + -4)

Reorder the terms:
45y + -1y + -10y2 = 2(y + -4)

Combine like terms: 45y + -1y = 44y
44y + -10y2 = 2(y + -4)

Reorder the terms:
44y + -10y2 = 2(-4 + y)
44y + -10y2 = (-4 * 2 + y * 2)
44y + -10y2 = (-8 + 2y)

Solving
44y + -10y2 = -8 + 2y

Solving for variable 'y'.

Reorder the terms:
8 + 44y + -2y + -10y2 = -8 + 2y + 8 + -2y

Combine like terms: 44y + -2y = 42y
8 + 42y + -10y2 = -8 + 2y + 8 + -2y

Reorder the terms:
8 + 42y + -10y2 = -8 + 8 + 2y + -2y

Combine like terms: -8 + 8 = 0
8 + 42y + -10y2 = 0 + 2y + -2y
8 + 42y + -10y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
8 + 42y + -10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 21y + -5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 21y + -5y2)' equal to zero and attempt to solve:

Simplifying
4 + 21y + -5y2 = 0

Solving
4 + 21y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.8 + -4.2y + y2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -4.2y + 0.8 + y2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -4.2y + y2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -4.2y + y2 = 0 + 0.8
-4.2y + y2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-4.2y + y2 = 0.8

The y term is -4.2y.  Take half its coefficient (-2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
-4.2y + 4.41 + y2 = 0.8 + 4.41

Reorder the terms:
4.41 + -4.2y + y2 = 0.8 + 4.41

Combine like terms: 0.8 + 4.41 = 5.21
4.41 + -4.2y + y2 = 5.21

Factor a perfect square on the left side:
(y + -2.1)(y + -2.1) = 5.21

Calculate the square root of the right side: 2.282542442

Break this problem into two subproblems by setting 
(y + -2.1) equal to 2.282542442 and -2.282542442.

Subproblem 1
y + -2.1 = 2.282542442

Simplifying
y + -2.1 = 2.282542442

Reorder the terms:
-2.1 + y = 2.282542442

Solving
-2.1 + y = 2.282542442

Solving for variable 'y'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + y = 2.282542442 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + y = 2.282542442 + 2.1
y = 2.282542442 + 2.1

Combine like terms: 2.282542442 + 2.1 = 4.382542442
y = 4.382542442

Simplifying
y = 4.382542442

Subproblem 2
y + -2.1 = -2.282542442

Simplifying
y + -2.1 = -2.282542442

Reorder the terms:
-2.1 + y = -2.282542442

Solving
-2.1 + y = -2.282542442

Solving for variable 'y'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + y = -2.282542442 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + y = -2.282542442 + 2.1
y = -2.282542442 + 2.1

Combine like terms: -2.282542442 + 2.1 = -0.182542442
y = -0.182542442

Simplifying
y = -0.182542442

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.382542442, -0.182542442}
Solution
y = {4.382542442, -0.182542442}