y^2-3y-5y-15=0

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Solution for y^2-3y-5y-15=0 equation: 


Simplifying
y2 + -3y + -5y + -15 = 0

Reorder the terms:
-15 + -3y + -5y + y2 = 0

Combine like terms: -3y + -5y = -8y
-15 + -8y + y2 = 0

Solving
-15 + -8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -8y + 15 + y2 = 0 + 15

Reorder the terms:
-15 + 15 + -8y + y2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -8y + y2 = 0 + 15
-8y + y2 = 0 + 15

Combine like terms: 0 + 15 = 15
-8y + y2 = 15

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = 15 + 16

Reorder the terms:
16 + -8y + y2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + -8y + y2 = 31

Factor a perfect square on the left side:
(y + -4)(y + -4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(y + -4) equal to 5.567764363 and -5.567764363.


Subproblem 1
y + -4 = 5.567764363

Simplifying
y + -4 = 5.567764363

Reorder the terms:
-4 + y = 5.567764363

Solving
-4 + y = 5.567764363

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + y = 5.567764363 + 4
y = 5.567764363 + 4

Combine like terms: 5.567764363 + 4 = 9.567764363
y = 9.567764363

Simplifying
y = 9.567764363


Subproblem 2
y + -4 = -5.567764363

Simplifying
y + -4 = -5.567764363

Reorder the terms:
-4 + y = -5.567764363

Solving
-4 + y = -5.567764363

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + y = -5.567764363 + 4
y = -5.567764363 + 4

Combine like terms: -5.567764363 + 4 = -1.567764363
y = -1.567764363

Simplifying
y = -1.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.567764363, -1.567764363}

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