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

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

Simplifying
(3 + -1y)(y + 4) = 3y + -5

Reorder the terms:
(3 + -1y)(4 + y) = 3y + -5

Multiply (3 + -1y) * (4 + y)
(3(4 + y) + -1y * (4 + y)) = 3y + -5
((4 * 3 + y * 3) + -1y * (4 + y)) = 3y + -5
((12 + 3y) + -1y * (4 + y)) = 3y + -5
(12 + 3y + (4 * -1y + y * -1y)) = 3y + -5
(12 + 3y + (-4y + -1y2)) = 3y + -5

Combine like terms: 3y + -4y = -1y
(12 + -1y + -1y2) = 3y + -5

Reorder the terms:
12 + -1y + -1y2 = -5 + 3y

Solving
12 + -1y + -1y2 = -5 + 3y

Solving for variable 'y'.

Reorder the terms:
12 + 5 + -1y + -3y + -1y2 = -5 + 3y + 5 + -3y

Combine like terms: 12 + 5 = 17
17 + -1y + -3y + -1y2 = -5 + 3y + 5 + -3y

Combine like terms: -1y + -3y = -4y
17 + -4y + -1y2 = -5 + 3y + 5 + -3y

Reorder the terms:
17 + -4y + -1y2 = -5 + 5 + 3y + -3y

Combine like terms: -5 + 5 = 0
17 + -4y + -1y2 = 0 + 3y + -3y
17 + -4y + -1y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
17 + -4y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-17 + 4y + y2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 4y + 17 + y2 = 0 + 17

Reorder the terms:
-17 + 17 + 4y + y2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 4y + y2 = 0 + 17
4y + y2 = 0 + 17

Combine like terms: 0 + 17 = 17
4y + y2 = 17

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 17 + 4

Reorder the terms:
4 + 4y + y2 = 17 + 4

Combine like terms: 17 + 4 = 21
4 + 4y + y2 = 21

Factor a perfect square on the left side:
(y + 2)(y + 2) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(y + 2) equal to 4.582575695 and -4.582575695.

Subproblem 1
y + 2 = 4.582575695

Simplifying
y + 2 = 4.582575695

Reorder the terms:
2 + y = 4.582575695

Solving
2 + y = 4.582575695

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = 4.582575695 + -2

Combine like terms: 2 + -2 = 0
0 + y = 4.582575695 + -2
y = 4.582575695 + -2

Combine like terms: 4.582575695 + -2 = 2.582575695
y = 2.582575695

Simplifying
y = 2.582575695

Subproblem 2
y + 2 = -4.582575695

Simplifying
y + 2 = -4.582575695

Reorder the terms:
2 + y = -4.582575695

Solving
2 + y = -4.582575695

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = -4.582575695 + -2

Combine like terms: 2 + -2 = 0
0 + y = -4.582575695 + -2
y = -4.582575695 + -2

Combine like terms: -4.582575695 + -2 = -6.582575695
y = -6.582575695

Simplifying
y = -6.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.582575695, -6.582575695}