3y(y-5)-2y(y-3)=-18

Solution for 3y(y-5)-2y(y-3)=-18 equation:

Simplifying
3y(y + -5) + -2y(y + -3) = -18

Reorder the terms:
3y(-5 + y) + -2y(y + -3) = -18
(-5 * 3y + y * 3y) + -2y(y + -3) = -18
(-15y + 3y2) + -2y(y + -3) = -18

Reorder the terms:
-15y + 3y2 + -2y(-3 + y) = -18
-15y + 3y2 + (-3 * -2y + y * -2y) = -18
-15y + 3y2 + (6y + -2y2) = -18

Reorder the terms:
-15y + 6y + 3y2 + -2y2 = -18

Combine like terms: -15y + 6y = -9y
-9y + 3y2 + -2y2 = -18

Combine like terms: 3y2 + -2y2 = 1y2
-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.
(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}