(9-y)y=18

Solution for (9-y)y=18 equation:

Simplifying
(9 + -1y) * y = 18

Reorder the terms for easier multiplication:
y(9 + -1y) = 18
(9 * y + -1y * y) = 18
(9y + -1y2) = 18

Solving
9y + -1y2 = 18

Solving for variable 'y'.

Reorder the terms:
-18 + 9y + -1y2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 9y + -1y2 = 0

Factor a trinomial.
(-6 + y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-6 + y)' equal to zero and attempt to solve:

Simplifying
-6 + y = 0

Solving
-6 + y = 0

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

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

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

Combine like terms: 0 + 6 = 6
y = 6

Simplifying
y = 6
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {6, 3}