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

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

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

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

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

Combine like terms: -4y + 30y = 26y
(-24 + 26y + 5y2) = 0

Solving
-24 + 26y + 5y2 = 0

Solving for variable 'y'.

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

Simplifying
4 + -5y = 0

Solving
4 + -5y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5y = 0 + -4

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

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

Divide each side by '-5'.
y = 0.8

Simplifying
y = 0.8
Solution
y = {-6, 0.8}