(4y+7)(6+y)=0

Solution for (4y+7)(6+y)=0 equation:

Simplifying
(4y + 7)(6 + y) = 0

Reorder the terms:
(7 + 4y)(6 + y) = 0

Multiply (7 + 4y) * (6 + y)
(7(6 + y) + 4y * (6 + y)) = 0
((6 * 7 + y * 7) + 4y * (6 + y)) = 0
((42 + 7y) + 4y * (6 + y)) = 0
(42 + 7y + (6 * 4y + y * 4y)) = 0
(42 + 7y + (24y + 4y2)) = 0

Combine like terms: 7y + 24y = 31y
(42 + 31y + 4y2) = 0

Solving
42 + 31y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + y)(7 + 4y) = 0

Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 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 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(7 + 4y)' equal to zero and attempt to solve:

Simplifying
7 + 4y = 0

Solving
7 + 4y = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4y = 0 + -7
4y = 0 + -7

Combine like terms: 0 + -7 = -7
4y = -7

Divide each side by '4'.
y = -1.75

Simplifying
y = -1.75
Solution
y = {-6, -1.75}