(y+-3)(y+-3)=89

Solution for (y+-3)(y+-3)=89 equation:

Simplifying
(y + -3)(y + -3) = 89

Reorder the terms:
(-3 + y)(y + -3) = 89

Reorder the terms:
(-3 + y)(-3 + y) = 89

Multiply (-3 + y) * (-3 + y)
(-3(-3 + y) + y(-3 + y)) = 89
((-3 * -3 + y * -3) + y(-3 + y)) = 89
((9 + -3y) + y(-3 + y)) = 89
(9 + -3y + (-3 * y + y * y)) = 89
(9 + -3y + (-3y + y2)) = 89

Combine like terms: -3y + -3y = -6y
(9 + -6y + y2) = 89

Solving
9 + -6y + y2 = 89

Solving for variable 'y'.

Reorder the terms:
9 + -89 + -6y + y2 = 89 + -89

Combine like terms: 9 + -89 = -80
-80 + -6y + y2 = 89 + -89

Combine like terms: 89 + -89 = 0
-80 + -6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -6y + 80 + y2 = 0 + 80

Reorder the terms:
-80 + 80 + -6y + y2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -6y + y2 = 0 + 80
-6y + y2 = 0 + 80

Combine like terms: 0 + 80 = 80
-6y + y2 = 80

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = 80 + 9

Reorder the terms:
9 + -6y + y2 = 80 + 9

Combine like terms: 80 + 9 = 89
9 + -6y + y2 = 89

Factor a perfect square on the left side:
(y + -3)(y + -3) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(y + -3) equal to 9.433981132 and -9.433981132.

Subproblem 1
y + -3 = 9.433981132

Simplifying
y + -3 = 9.433981132

Reorder the terms:
-3 + y = 9.433981132

Solving
-3 + y = 9.433981132

Solving for variable 'y'.

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

Add '3' to each side of the equation.
-3 + 3 + y = 9.433981132 + 3

Combine like terms: -3 + 3 = 0
0 + y = 9.433981132 + 3
y = 9.433981132 + 3

Combine like terms: 9.433981132 + 3 = 12.433981132
y = 12.433981132

Simplifying
y = 12.433981132

Subproblem 2
y + -3 = -9.433981132

Simplifying
y + -3 = -9.433981132

Reorder the terms:
-3 + y = -9.433981132

Solving
-3 + y = -9.433981132

Solving for variable 'y'.

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

Add '3' to each side of the equation.
-3 + 3 + y = -9.433981132 + 3

Combine like terms: -3 + 3 = 0
0 + y = -9.433981132 + 3
y = -9.433981132 + 3

Combine like terms: -9.433981132 + 3 = -6.433981132
y = -6.433981132

Simplifying
y = -6.433981132

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.433981132, -6.433981132}