(6+y)(4y+2)=0

Solution for (6+y)(4y+2)=0 equation:

Simplifying
(6 + y)(4y + 2) = 0

Reorder the terms:
(6 + y)(2 + 4y) = 0

Multiply (6 + y) * (2 + 4y)
(6(2 + 4y) + y(2 + 4y)) = 0
((2 * 6 + 4y * 6) + y(2 + 4y)) = 0
((12 + 24y) + y(2 + 4y)) = 0
(12 + 24y + (2 * y + 4y * y)) = 0
(12 + 24y + (2y + 4y2)) = 0

Combine like terms: 24y + 2y = 26y
(12 + 26y + 4y2) = 0

Solving
12 + 26y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 13y + 2y2) = 0

Factor a trinomial.
2((6 + y)(1 + 2y)) = 0

Ignore the factor 2.
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 '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {-6, -0.5}