6=3+5y(y-2)

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

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

Reorder the terms:
6 = 3 + 5y(-2 + y)
6 = 3 + (-2 * 5y + y * 5y)
6 = 3 + (-10y + 5y2)

Solving
6 = 3 + -10y + 5y2

Solving for variable 'y'.

Combine like terms: 6 + -3 = 3
3 + 10y + -5y2 = 3 + -10y + 5y2 + -3 + 10y + -5y2

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

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

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

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

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.6 + -2y + y2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2y + 0.6 + y2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2y + y2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2y + y2 = 0 + 0.6
-2y + y2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2y + y2 = 0.6

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 0.6 + 1

Reorder the terms:
1 + -2y + y2 = 0.6 + 1

Combine like terms: 0.6 + 1 = 1.6
1 + -2y + y2 = 1.6

Factor a perfect square on the left side:
(y + -1)(y + -1) = 1.6

Calculate the square root of the right side: 1.264911064

Break this problem into two subproblems by setting 
(y + -1) equal to 1.264911064 and -1.264911064.

Subproblem 1
y + -1 = 1.264911064

Simplifying
y + -1 = 1.264911064

Reorder the terms:
-1 + y = 1.264911064

Solving
-1 + y = 1.264911064

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 1.264911064 + 1

Combine like terms: -1 + 1 = 0
0 + y = 1.264911064 + 1
y = 1.264911064 + 1

Combine like terms: 1.264911064 + 1 = 2.264911064
y = 2.264911064

Simplifying
y = 2.264911064

Subproblem 2
y + -1 = -1.264911064

Simplifying
y + -1 = -1.264911064

Reorder the terms:
-1 + y = -1.264911064

Solving
-1 + y = -1.264911064

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -1.264911064 + 1

Combine like terms: -1 + 1 = 0
0 + y = -1.264911064 + 1
y = -1.264911064 + 1

Combine like terms: -1.264911064 + 1 = -0.264911064
y = -0.264911064

Simplifying
y = -0.264911064

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.264911064, -0.264911064}