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

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

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

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

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

Combine like terms: 24y + 7y = 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}