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

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

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

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

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

Reorder the terms for easier multiplication:
-3 + 8y = 5 * 3y(-1 + y)

Multiply 5 * 3
-3 + 8y = 15y(-1 + y)
-3 + 8y = (-1 * 15y + y * 15y)
-3 + 8y = (-15y + 15y2)

Solving
-3 + 8y = -15y + 15y2

Solving for variable 'y'.

Combine like terms: 8y + 15y = 23y
-3 + 23y + -15y2 = -15y + 15y2 + 15y + -15y2

Reorder the terms:
-3 + 23y + -15y2 = -15y + 15y + 15y2 + -15y2

Combine like terms: -15y + 15y = 0
-3 + 23y + -15y2 = 0 + 15y2 + -15y2
-3 + 23y + -15y2 = 15y2 + -15y2

Combine like terms: 15y2 + -15y2 = 0
-3 + 23y + -15y2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
0.2 + -1.533333333y + y2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.533333333y + -0.2 + y2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.533333333y + y2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.533333333y + y2 = 0 + -0.2
-1.533333333y + y2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1.533333333y + y2 = -0.2

The y term is -1.533333333y.  Take half its coefficient (-0.7666666665).
Square it (0.5877777775) and add it to both sides.

Add '0.5877777775' to each side of the equation.
-1.533333333y + 0.5877777775 + y2 = -0.2 + 0.5877777775

Reorder the terms:
0.5877777775 + -1.533333333y + y2 = -0.2 + 0.5877777775

Combine like terms: -0.2 + 0.5877777775 = 0.3877777775
0.5877777775 + -1.533333333y + y2 = 0.3877777775

Factor a perfect square on the left side:
(y + -0.7666666665)(y + -0.7666666665) = 0.3877777775

Calculate the square root of the right side: 0.622718056

Break this problem into two subproblems by setting 
(y + -0.7666666665) equal to 0.622718056 and -0.622718056.

Subproblem 1
y + -0.7666666665 = 0.622718056

Simplifying
y + -0.7666666665 = 0.622718056

Reorder the terms:
-0.7666666665 + y = 0.622718056

Solving
-0.7666666665 + y = 0.622718056

Solving for variable 'y'.

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

Add '0.7666666665' to each side of the equation.
-0.7666666665 + 0.7666666665 + y = 0.622718056 + 0.7666666665

Combine like terms: -0.7666666665 + 0.7666666665 = 0.0000000000
0.0000000000 + y = 0.622718056 + 0.7666666665
y = 0.622718056 + 0.7666666665

Combine like terms: 0.622718056 + 0.7666666665 = 1.3893847225
y = 1.3893847225

Simplifying
y = 1.3893847225

Subproblem 2
y + -0.7666666665 = -0.622718056

Simplifying
y + -0.7666666665 = -0.622718056

Reorder the terms:
-0.7666666665 + y = -0.622718056

Solving
-0.7666666665 + y = -0.622718056

Solving for variable 'y'.

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

Add '0.7666666665' to each side of the equation.
-0.7666666665 + 0.7666666665 + y = -0.622718056 + 0.7666666665

Combine like terms: -0.7666666665 + 0.7666666665 = 0.0000000000
0.0000000000 + y = -0.622718056 + 0.7666666665
y = -0.622718056 + 0.7666666665

Combine like terms: -0.622718056 + 0.7666666665 = 0.1439486105
y = 0.1439486105

Simplifying
y = 0.1439486105

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.3893847225, 0.1439486105}