-5y(y+4)=17+3y

Solution for -5y(y+4)=17+3y equation:

Simplifying
-5y(y + 4) = 17 + 3y

Reorder the terms:
-5y(4 + y) = 17 + 3y
(4 * -5y + y * -5y) = 17 + 3y
(-20y + -5y2) = 17 + 3y

Solving
-20y + -5y2 = 17 + 3y

Solving for variable 'y'.

Reorder the terms:
-17 + -20y + -3y + -5y2 = 17 + 3y + -17 + -3y

Combine like terms: -20y + -3y = -23y
-17 + -23y + -5y2 = 17 + 3y + -17 + -3y

Reorder the terms:
-17 + -23y + -5y2 = 17 + -17 + 3y + -3y

Combine like terms: 17 + -17 = 0
-17 + -23y + -5y2 = 0 + 3y + -3y
-17 + -23y + -5y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-17 + -23y + -5y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(17 + 23y + 5y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(17 + 23y + 5y2)' equal to zero and attempt to solve:

Simplifying
17 + 23y + 5y2 = 0

Solving
17 + 23y + 5y2 = 0

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

Divide each side by '5'.
3.4 + 4.6y + y2 = 0

Move the constant term to the right:

Add '-3.4' to each side of the equation.
3.4 + 4.6y + -3.4 + y2 = 0 + -3.4

Reorder the terms:
3.4 + -3.4 + 4.6y + y2 = 0 + -3.4

Combine like terms: 3.4 + -3.4 = 0.0
0.0 + 4.6y + y2 = 0 + -3.4
4.6y + y2 = 0 + -3.4

Combine like terms: 0 + -3.4 = -3.4
4.6y + y2 = -3.4

The y term is 4.6y.  Take half its coefficient (2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
4.6y + 5.29 + y2 = -3.4 + 5.29

Reorder the terms:
5.29 + 4.6y + y2 = -3.4 + 5.29

Combine like terms: -3.4 + 5.29 = 1.89
5.29 + 4.6y + y2 = 1.89

Factor a perfect square on the left side:
(y + 2.3)(y + 2.3) = 1.89

Calculate the square root of the right side: 1.374772708

Break this problem into two subproblems by setting 
(y + 2.3) equal to 1.374772708 and -1.374772708.

Subproblem 1
y + 2.3 = 1.374772708

Simplifying
y + 2.3 = 1.374772708

Reorder the terms:
2.3 + y = 1.374772708

Solving
2.3 + y = 1.374772708

Solving for variable 'y'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + y = 1.374772708 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + y = 1.374772708 + -2.3
y = 1.374772708 + -2.3

Combine like terms: 1.374772708 + -2.3 = -0.925227292
y = -0.925227292

Simplifying
y = -0.925227292

Subproblem 2
y + 2.3 = -1.374772708

Simplifying
y + 2.3 = -1.374772708

Reorder the terms:
2.3 + y = -1.374772708

Solving
2.3 + y = -1.374772708

Solving for variable 'y'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + y = -1.374772708 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + y = -1.374772708 + -2.3
y = -1.374772708 + -2.3

Combine like terms: -1.374772708 + -2.3 = -3.674772708
y = -3.674772708

Simplifying
y = -3.674772708

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.925227292, -3.674772708}
Solution
y = {-0.925227292, -3.674772708}