(1[5y+9]1)(1[3-y]1)=0

Solution for (1[5y+9]1)(1[3-y]1)=0 equation:

Simplifying
(1[5y + 9] * 1)(1[3 + -1y] * 1) = 0

Reorder the terms:
(1[9 + 5y] * 1)(1[3 + -1y] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[9 + 5y])(1[3 + -1y] * 1) = 0

Multiply 1 * 1
(1[9 + 5y])(1[3 + -1y] * 1) = 0
([9 * 1 + 5y * 1])(1[3 + -1y] * 1) = 0
([9 + 5y])(1[3 + -1y] * 1) = 0

Reorder the terms for easier multiplication:
(9 + 5y)(1 * 1[3 + -1y]) = 0

Multiply 1 * 1
(9 + 5y)(1[3 + -1y]) = 0
(9 + 5y)([3 * 1 + -1y * 1]) = 0
(9 + 5y)([3 + -1y]) = 0

Multiply (9 + 5y) * (3 + -1y)
(9(3 + -1y) + 5y * (3 + -1y)) = 0
((3 * 9 + -1y * 9) + 5y * (3 + -1y)) = 0
((27 + -9y) + 5y * (3 + -1y)) = 0
(27 + -9y + (3 * 5y + -1y * 5y)) = 0
(27 + -9y + (15y + -5y2)) = 0

Combine like terms: -9y + 15y = 6y
(27 + 6y + -5y2) = 0

Solving
27 + 6y + -5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + -1y)(9 + 5y) = 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 '(9 + 5y)' equal to zero and attempt to solve:

Simplifying
9 + 5y = 0

Solving
9 + 5y = 0

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

Add '-9' to each side of the equation.
9 + -9 + 5y = 0 + -9

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

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

Divide each side by '5'.
y = -1.8

Simplifying
y = -1.8
Solution
y = {3, -1.8}