(4y-5)(6+y)=0

Solution for (4y-5)(6+y)=0 equation:

Simplifying
(4y + -5)(6 + y) = 0

Reorder the terms:
(-5 + 4y)(6 + y) = 0

Multiply (-5 + 4y) * (6 + y)
(-5(6 + y) + 4y * (6 + y)) = 0
((6 * -5 + y * -5) + 4y * (6 + y)) = 0
((-30 + -5y) + 4y * (6 + y)) = 0
(-30 + -5y + (6 * 4y + y * 4y)) = 0
(-30 + -5y + (24y + 4y2)) = 0

Combine like terms: -5y + 24y = 19y
(-30 + 19y + 4y2) = 0

Solving
-30 + 19y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + -1y)(5 + -4y) = 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 + -4y)' equal to zero and attempt to solve:

Simplifying
5 + -4y = 0

Solving
5 + -4y = 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 + -4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4y = 0 + -5
-4y = 0 + -5

Combine like terms: 0 + -5 = -5
-4y = -5

Divide each side by '-4'.
y = 1.25

Simplifying
y = 1.25
Solution
y = {-6, 1.25}