y(y-3)=18

Solution for y(y-3)=18 equation:

Simplifying
y(y + -3) = 18

Reorder the terms:
y(-3 + y) = 18
(-3 * y + y * y) = 18
(-3y + y2) = 18

Solving
-3y + y2 = 18

Solving for variable 'y'.

Reorder the terms:
-18 + -3y + y2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -3y + y2 = 0

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

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

Simplifying
6 + -1y = 0

Solving
6 + -1y = 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 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

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