(2y+5)(6-y)=0

Solution for (2y+5)(6-y)=0 equation:

Simplifying
(2y + 5)(6 + -1y) = 0

Reorder the terms:
(5 + 2y)(6 + -1y) = 0

Multiply (5 + 2y) * (6 + -1y)
(5(6 + -1y) + 2y * (6 + -1y)) = 0
((6 * 5 + -1y * 5) + 2y * (6 + -1y)) = 0
((30 + -5y) + 2y * (6 + -1y)) = 0
(30 + -5y + (6 * 2y + -1y * 2y)) = 0
(30 + -5y + (12y + -2y2)) = 0

Combine like terms: -5y + 12y = 7y
(30 + 7y + -2y2) = 0

Solving
30 + 7y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + -1y)(5 + 2y) = 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 '(5 + 2y)' equal to zero and attempt to solve:

Simplifying
5 + 2y = 0

Solving
5 + 2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2y = 0 + -5
2y = 0 + -5

Combine like terms: 0 + -5 = -5
2y = -5

Divide each side by '2'.
y = -2.5

Simplifying
y = -2.5
Solution
y = {6, -2.5}