y(y+5)+2(y-3)=

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Solution for y(y+5)+2(y-3)= equation: 


Simplifying
y(y + 5) + 2(y + -3) = 0

Reorder the terms:
y(5 + y) + 2(y + -3) = 0
(5 * y + y * y) + 2(y + -3) = 0
(5y + y2) + 2(y + -3) = 0

Reorder the terms:
5y + y2 + 2(-3 + y) = 0
5y + y2 + (-3 * 2 + y * 2) = 0
5y + y2 + (-6 + 2y) = 0

Reorder the terms:
-6 + 5y + 2y + y2 = 0

Combine like terms: 5y + 2y = 7y
-6 + 7y + y2 = 0

Solving
-6 + 7y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 7y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + 7y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7y + y2 = 0 + 6
7y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
7y + y2 = 6

The y term is 7y.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7y + 12.25 + y2 = 6 + 12.25

Reorder the terms:
12.25 + 7y + y2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + 7y + y2 = 18.25

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(y + 3.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
y + 3.5 = 4.272001873

Simplifying
y + 3.5 = 4.272001873

Reorder the terms:
3.5 + y = 4.272001873

Solving
3.5 + y = 4.272001873

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = 4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 4.272001873 + -3.5
y = 4.272001873 + -3.5

Combine like terms: 4.272001873 + -3.5 = 0.772001873
y = 0.772001873

Simplifying
y = 0.772001873


Subproblem 2
y + 3.5 = -4.272001873

Simplifying
y + 3.5 = -4.272001873

Reorder the terms:
3.5 + y = -4.272001873

Solving
3.5 + y = -4.272001873

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = -4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -4.272001873 + -3.5
y = -4.272001873 + -3.5

Combine like terms: -4.272001873 + -3.5 = -7.772001873
y = -7.772001873

Simplifying
y = -7.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.772001873, -7.772001873}

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