6y-5=(y+2)*(y-3)

Solution for 6y-5=(y+2)*(y-3) equation:

Simplifying
6y + -5 = (y + 2)(y + -3)

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

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

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

Multiply (2 + y) * (-3 + y)
-5 + 6y = (2(-3 + y) + y(-3 + y))
-5 + 6y = ((-3 * 2 + y * 2) + y(-3 + y))
-5 + 6y = ((-6 + 2y) + y(-3 + y))
-5 + 6y = (-6 + 2y + (-3 * y + y * y))
-5 + 6y = (-6 + 2y + (-3y + y2))

Combine like terms: 2y + -3y = -1y
-5 + 6y = (-6 + -1y + y2)

Solving
-5 + 6y = -6 + -1y + y2

Solving for variable 'y'.

Reorder the terms:
-5 + 6 + 6y + y + -1y2 = -6 + -1y + y2 + 6 + y + -1y2

Combine like terms: -5 + 6 = 1
1 + 6y + y + -1y2 = -6 + -1y + y2 + 6 + y + -1y2

Combine like terms: 6y + y = 7y
1 + 7y + -1y2 = -6 + -1y + y2 + 6 + y + -1y2

Reorder the terms:
1 + 7y + -1y2 = -6 + 6 + -1y + y + y2 + -1y2

Combine like terms: -6 + 6 = 0
1 + 7y + -1y2 = 0 + -1y + y + y2 + -1y2
1 + 7y + -1y2 = -1y + y + y2 + -1y2

Combine like terms: -1y + y = 0
1 + 7y + -1y2 = 0 + y2 + -1y2
1 + 7y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
1 + 7y + -1y2 = 0

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

Divide each side by '-1'.
-1 + -7y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -7y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -7y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7y + y2 = 0 + 1
-7y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-7y + y2 = 1

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 = 1 + 12.25

Reorder the terms:
12.25 + -7y + y2 = 1 + 12.25

Combine like terms: 1 + 12.25 = 13.25
12.25 + -7y + y2 = 13.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(y + -3.5) equal to 3.640054945 and -3.640054945.

Subproblem 1
y + -3.5 = 3.640054945

Simplifying
y + -3.5 = 3.640054945

Reorder the terms:
-3.5 + y = 3.640054945

Solving
-3.5 + y = 3.640054945

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 = 3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 3.640054945 + 3.5
y = 3.640054945 + 3.5

Combine like terms: 3.640054945 + 3.5 = 7.140054945
y = 7.140054945

Simplifying
y = 7.140054945

Subproblem 2
y + -3.5 = -3.640054945

Simplifying
y + -3.5 = -3.640054945

Reorder the terms:
-3.5 + y = -3.640054945

Solving
-3.5 + y = -3.640054945

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 = -3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -3.640054945 + 3.5
y = -3.640054945 + 3.5

Combine like terms: -3.640054945 + 3.5 = -0.140054945
y = -0.140054945

Simplifying
y = -0.140054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.140054945, -0.140054945}