(y-2)(y-3)=9y+6

Solution for (y-2)(y-3)=9y+6 equation:

Simplifying
(y + -2)(y + -3) = 9y + 6

Reorder the terms:
(-2 + y)(y + -3) = 9y + 6

Reorder the terms:
(-2 + y)(-3 + y) = 9y + 6

Multiply (-2 + y) * (-3 + y)
(-2(-3 + y) + y(-3 + y)) = 9y + 6
((-3 * -2 + y * -2) + y(-3 + y)) = 9y + 6
((6 + -2y) + y(-3 + y)) = 9y + 6
(6 + -2y + (-3 * y + y * y)) = 9y + 6
(6 + -2y + (-3y + y2)) = 9y + 6

Combine like terms: -2y + -3y = -5y
(6 + -5y + y2) = 9y + 6

Reorder the terms:
6 + -5y + y2 = 6 + 9y

Add '-6' to each side of the equation.
6 + -5y + -6 + y2 = 6 + -6 + 9y

Reorder the terms:
6 + -6 + -5y + y2 = 6 + -6 + 9y

Combine like terms: 6 + -6 = 0
0 + -5y + y2 = 6 + -6 + 9y
-5y + y2 = 6 + -6 + 9y

Combine like terms: 6 + -6 = 0
-5y + y2 = 0 + 9y
-5y + y2 = 9y

Solving
-5y + y2 = 9y

Solving for variable 'y'.

Reorder the terms:
-5y + -9y + y2 = 9y + -9y

Combine like terms: -5y + -9y = -14y
-14y + y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
-14y + y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-14 + y) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-14 + y)' equal to zero and attempt to solve:

Simplifying
-14 + y = 0

Solving
-14 + y = 0

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

Add '14' to each side of the equation.
-14 + 14 + y = 0 + 14

Combine like terms: -14 + 14 = 0
0 + y = 0 + 14
y = 0 + 14

Combine like terms: 0 + 14 = 14
y = 14

Simplifying
y = 14
Solution
y = {0, 14}