Simplifying
(y + 9)(y + -2) = 4y
Reorder the terms:
(9 + y)(y + -2) = 4y
Reorder the terms:
(9 + y)(-2 + y) = 4y
Multiply (9 + y) * (-2 + y)
(9(-2 + y) + y(-2 + y)) = 4y
((-2 * 9 + y * 9) + y(-2 + y)) = 4y
((-18 + 9y) + y(-2 + y)) = 4y
(-18 + 9y + (-2 * y + y * y)) = 4y
(-18 + 9y + (-2y + y^{2})) = 4y
Combine like terms: 9y + -2y = 7y
(-18 + 7y + y^{2}) = 4y
Solving
-18 + 7y + y^{2} = 4y
Solving for variable 'y'.
Reorder the terms:
-18 + 7y + -4y + y^{2} = 4y + -4y
Combine like terms: 7y + -4y = 3y
-18 + 3y + y^{2} = 4y + -4y
Combine like terms: 4y + -4y = 0
-18 + 3y + y^{2} = 0
Factor a trinomial.
(-6 + -1y)(3 + -1y) = 0
#### Subproblem 1

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
#### 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}