y^2+9y-32=0

Solution for y^2+9y-32=0 equation:

Simplifying
y2 + 9y + -32 = 0

Reorder the terms:
-32 + 9y + y2 = 0

Solving
-32 + 9y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 9y + 32 + y2 = 0 + 32

Reorder the terms:
-32 + 32 + 9y + y2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 9y + y2 = 0 + 32
9y + y2 = 0 + 32

Combine like terms: 0 + 32 = 32
9y + y2 = 32

The y term is 9y.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9y + 20.25 + y2 = 32 + 20.25

Reorder the terms:
20.25 + 9y + y2 = 32 + 20.25

Combine like terms: 32 + 20.25 = 52.25
20.25 + 9y + y2 = 52.25

Factor a perfect square on the left side:
(y + 4.5)(y + 4.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(y + 4.5) equal to 7.228416147 and -7.228416147.

Subproblem 1
y + 4.5 = 7.228416147

Simplifying
y + 4.5 = 7.228416147

Reorder the terms:
4.5 + y = 7.228416147

Solving
4.5 + y = 7.228416147

Solving for variable 'y'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = 7.228416147 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = 7.228416147 + -4.5
y = 7.228416147 + -4.5

Combine like terms: 7.228416147 + -4.5 = 2.728416147
y = 2.728416147

Simplifying
y = 2.728416147

Subproblem 2
y + 4.5 = -7.228416147

Simplifying
y + 4.5 = -7.228416147

Reorder the terms:
4.5 + y = -7.228416147

Solving
4.5 + y = -7.228416147

Solving for variable 'y'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = -7.228416147 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = -7.228416147 + -4.5
y = -7.228416147 + -4.5

Combine like terms: -7.228416147 + -4.5 = -11.728416147
y = -11.728416147

Simplifying
y = -11.728416147

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.728416147, -11.728416147}