165=y(y-2)

Solution for 165=y(y-2) equation:

Simplifying
165 = y(y + -2)

Reorder the terms:
165 = y(-2 + y)
165 = (-2 * y + y * y)
165 = (-2y + y2)

Solving
165 = -2y + y2

Solving for variable 'y'.

Reorder the terms:
165 + 2y + -1y2 = -2y + 2y + y2 + -1y2

Combine like terms: -2y + 2y = 0
165 + 2y + -1y2 = 0 + y2 + -1y2
165 + 2y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
165 + 2y + -1y2 = 0

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

Divide each side by '-1'.
-165 + -2y + y2 = 0

Move the constant term to the right:

Add '165' to each side of the equation.
-165 + -2y + 165 + y2 = 0 + 165

Reorder the terms:
-165 + 165 + -2y + y2 = 0 + 165

Combine like terms: -165 + 165 = 0
0 + -2y + y2 = 0 + 165
-2y + y2 = 0 + 165

Combine like terms: 0 + 165 = 165
-2y + y2 = 165

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 = 165 + 1

Reorder the terms:
1 + -2y + y2 = 165 + 1

Combine like terms: 165 + 1 = 166
1 + -2y + y2 = 166

Factor a perfect square on the left side:
(y + -1)(y + -1) = 166

Calculate the square root of the right side: 12.884098727

Break this problem into two subproblems by setting 
(y + -1) equal to 12.884098727 and -12.884098727.

Subproblem 1
y + -1 = 12.884098727

Simplifying
y + -1 = 12.884098727

Reorder the terms:
-1 + y = 12.884098727

Solving
-1 + y = 12.884098727

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 = 12.884098727 + 1

Combine like terms: -1 + 1 = 0
0 + y = 12.884098727 + 1
y = 12.884098727 + 1

Combine like terms: 12.884098727 + 1 = 13.884098727
y = 13.884098727

Simplifying
y = 13.884098727

Subproblem 2
y + -1 = -12.884098727

Simplifying
y + -1 = -12.884098727

Reorder the terms:
-1 + y = -12.884098727

Solving
-1 + y = -12.884098727

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 = -12.884098727 + 1

Combine like terms: -1 + 1 = 0
0 + y = -12.884098727 + 1
y = -12.884098727 + 1

Combine like terms: -12.884098727 + 1 = -11.884098727
y = -11.884098727

Simplifying
y = -11.884098727

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {13.884098727, -11.884098727}