y^2-6y-18=0

Solution for y^2-6y-18=0 equation:

Simplifying
y2 + -6y + -18 = 0

Reorder the terms:
-18 + -6y + y2 = 0

Solving
-18 + -6y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -6y + 18 + y2 = 0 + 18

Reorder the terms:
-18 + 18 + -6y + y2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -6y + y2 = 0 + 18
-6y + y2 = 0 + 18

Combine like terms: 0 + 18 = 18
-6y + y2 = 18

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 = 18 + 9

Reorder the terms:
9 + -6y + y2 = 18 + 9

Combine like terms: 18 + 9 = 27
9 + -6y + y2 = 27

Factor a perfect square on the left side:
(y + -3)(y + -3) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(y + -3) equal to 5.196152423 and -5.196152423.

Subproblem 1
y + -3 = 5.196152423

Simplifying
y + -3 = 5.196152423

Reorder the terms:
-3 + y = 5.196152423

Solving
-3 + y = 5.196152423

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 = 5.196152423 + 3

Combine like terms: -3 + 3 = 0
0 + y = 5.196152423 + 3
y = 5.196152423 + 3

Combine like terms: 5.196152423 + 3 = 8.196152423
y = 8.196152423

Simplifying
y = 8.196152423

Subproblem 2
y + -3 = -5.196152423

Simplifying
y + -3 = -5.196152423

Reorder the terms:
-3 + y = -5.196152423

Solving
-3 + y = -5.196152423

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 = -5.196152423 + 3

Combine like terms: -3 + 3 = 0
0 + y = -5.196152423 + 3
y = -5.196152423 + 3

Combine like terms: -5.196152423 + 3 = -2.196152423
y = -2.196152423

Simplifying
y = -2.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.196152423, -2.196152423}