8(y-1)(y+3)=5(y-2)(y+1)

Solution for 8(y-1)(y+3)=5(y-2)(y+1) equation:

Simplifying
8(y + -1)(y + 3) = 5(y + -2)(y + 1)

Reorder the terms:
8(-1 + y)(y + 3) = 5(y + -2)(y + 1)

Reorder the terms:
8(-1 + y)(3 + y) = 5(y + -2)(y + 1)

Multiply (-1 + y) * (3 + y)
8(-1(3 + y) + y(3 + y)) = 5(y + -2)(y + 1)
8((3 * -1 + y * -1) + y(3 + y)) = 5(y + -2)(y + 1)
8((-3 + -1y) + y(3 + y)) = 5(y + -2)(y + 1)
8(-3 + -1y + (3 * y + y * y)) = 5(y + -2)(y + 1)
8(-3 + -1y + (3y + y2)) = 5(y + -2)(y + 1)

Combine like terms: -1y + 3y = 2y
8(-3 + 2y + y2) = 5(y + -2)(y + 1)
(-3 * 8 + 2y * 8 + y2 * 8) = 5(y + -2)(y + 1)
(-24 + 16y + 8y2) = 5(y + -2)(y + 1)

Reorder the terms:
-24 + 16y + 8y2 = 5(-2 + y)(y + 1)

Reorder the terms:
-24 + 16y + 8y2 = 5(-2 + y)(1 + y)

Multiply (-2 + y) * (1 + y)
-24 + 16y + 8y2 = 5(-2(1 + y) + y(1 + y))
-24 + 16y + 8y2 = 5((1 * -2 + y * -2) + y(1 + y))
-24 + 16y + 8y2 = 5((-2 + -2y) + y(1 + y))
-24 + 16y + 8y2 = 5(-2 + -2y + (1 * y + y * y))
-24 + 16y + 8y2 = 5(-2 + -2y + (1y + y2))

Combine like terms: -2y + 1y = -1y
-24 + 16y + 8y2 = 5(-2 + -1y + y2)
-24 + 16y + 8y2 = (-2 * 5 + -1y * 5 + y2 * 5)
-24 + 16y + 8y2 = (-10 + -5y + 5y2)

Solving
-24 + 16y + 8y2 = -10 + -5y + 5y2

Solving for variable 'y'.

Reorder the terms:
-24 + 10 + 16y + 5y + 8y2 + -5y2 = -10 + -5y + 5y2 + 10 + 5y + -5y2

Combine like terms: -24 + 10 = -14
-14 + 16y + 5y + 8y2 + -5y2 = -10 + -5y + 5y2 + 10 + 5y + -5y2

Combine like terms: 16y + 5y = 21y
-14 + 21y + 8y2 + -5y2 = -10 + -5y + 5y2 + 10 + 5y + -5y2

Combine like terms: 8y2 + -5y2 = 3y2
-14 + 21y + 3y2 = -10 + -5y + 5y2 + 10 + 5y + -5y2

Reorder the terms:
-14 + 21y + 3y2 = -10 + 10 + -5y + 5y + 5y2 + -5y2

Combine like terms: -10 + 10 = 0
-14 + 21y + 3y2 = 0 + -5y + 5y + 5y2 + -5y2
-14 + 21y + 3y2 = -5y + 5y + 5y2 + -5y2

Combine like terms: -5y + 5y = 0
-14 + 21y + 3y2 = 0 + 5y2 + -5y2
-14 + 21y + 3y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
-14 + 21y + 3y2 = 0

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

Divide each side by '3'.
-4.666666667 + 7y + y2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + 7y + 4.666666667 + y2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + 7y + y2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + 7y + y2 = 0 + 4.666666667
7y + y2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
7y + y2 = 4.666666667

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 = 4.666666667 + 12.25

Reorder the terms:
12.25 + 7y + y2 = 4.666666667 + 12.25

Combine like terms: 4.666666667 + 12.25 = 16.916666667
12.25 + 7y + y2 = 16.916666667

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 16.916666667

Calculate the square root of the right side: 4.11298756

Break this problem into two subproblems by setting 
(y + 3.5) equal to 4.11298756 and -4.11298756.

Subproblem 1
y + 3.5 = 4.11298756

Simplifying
y + 3.5 = 4.11298756

Reorder the terms:
3.5 + y = 4.11298756

Solving
3.5 + y = 4.11298756

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 = 4.11298756 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 4.11298756 + -3.5
y = 4.11298756 + -3.5

Combine like terms: 4.11298756 + -3.5 = 0.61298756
y = 0.61298756

Simplifying
y = 0.61298756

Subproblem 2
y + 3.5 = -4.11298756

Simplifying
y + 3.5 = -4.11298756

Reorder the terms:
3.5 + y = -4.11298756

Solving
3.5 + y = -4.11298756

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 = -4.11298756 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -4.11298756 + -3.5
y = -4.11298756 + -3.5

Combine like terms: -4.11298756 + -3.5 = -7.61298756
y = -7.61298756

Simplifying
y = -7.61298756

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.61298756, -7.61298756}