13=2y(y-2)+5

Solution for 13=2y(y-2)+5 equation:

Simplifying
13 = 2y(y + -2) + 5

Reorder the terms:
13 = 2y(-2 + y) + 5
13 = (-2 * 2y + y * 2y) + 5
13 = (-4y + 2y2) + 5

Reorder the terms:
13 = 5 + -4y + 2y2

Solving
13 = 5 + -4y + 2y2

Solving for variable 'y'.

Combine like terms: 13 + -5 = 8
8 + 4y + -2y2 = 5 + -4y + 2y2 + -5 + 4y + -2y2

Reorder the terms:
8 + 4y + -2y2 = 5 + -5 + -4y + 4y + 2y2 + -2y2

Combine like terms: 5 + -5 = 0
8 + 4y + -2y2 = 0 + -4y + 4y + 2y2 + -2y2
8 + 4y + -2y2 = -4y + 4y + 2y2 + -2y2

Combine like terms: -4y + 4y = 0
8 + 4y + -2y2 = 0 + 2y2 + -2y2
8 + 4y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
8 + 4y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 2y + -1y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 2y + -1y2)' equal to zero and attempt to solve:

Simplifying
4 + 2y + -1y2 = 0

Solving
4 + 2y + -1y2 = 0

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

Divide each side by '-1'.
-4 + -2y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -2y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2y + y2 = 0 + 4
-2y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2y + y2 = 4

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 = 4 + 1

Reorder the terms:
1 + -2y + y2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2y + y2 = 5

Factor a perfect square on the left side:
(y + -1)(y + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(y + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
y + -1 = 2.236067978

Simplifying
y + -1 = 2.236067978

Reorder the terms:
-1 + y = 2.236067978

Solving
-1 + y = 2.236067978

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 = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + y = 2.236067978 + 1
y = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
y = 3.236067978

Simplifying
y = 3.236067978

Subproblem 2
y + -1 = -2.236067978

Simplifying
y + -1 = -2.236067978

Reorder the terms:
-1 + y = -2.236067978

Solving
-1 + y = -2.236067978

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 = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + y = -2.236067978 + 1
y = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
y = -1.236067978

Simplifying
y = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.236067978, -1.236067978}
Solution
y = {3.236067978, -1.236067978}