(5y-8)(6+y)=0

Solution for (5y-8)(6+y)=0 equation:

Simplifying
(5y + -8)(6 + y) = 0

Reorder the terms:
(-8 + 5y)(6 + y) = 0

Multiply (-8 + 5y) * (6 + y)
(-8(6 + y) + 5y * (6 + y)) = 0
((6 * -8 + y * -8) + 5y * (6 + y)) = 0
((-48 + -8y) + 5y * (6 + y)) = 0
(-48 + -8y + (6 * 5y + y * 5y)) = 0
(-48 + -8y + (30y + 5y2)) = 0

Combine like terms: -8y + 30y = 22y
(-48 + 22y + 5y2) = 0

Solving
-48 + 22y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + -1y)(8 + -5y) = 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 '(8 + -5y)' equal to zero and attempt to solve:

Simplifying
8 + -5y = 0

Solving
8 + -5y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5y = 0 + -8
-5y = 0 + -8

Combine like terms: 0 + -8 = -8
-5y = -8

Divide each side by '-5'.
y = 1.6

Simplifying
y = 1.6
Solution
y = {-6, 1.6}