(4y-2)(3+y)=0

Solution for (4y-2)(3+y)=0 equation:

Simplifying
(4y + -2)(3 + y) = 0

Reorder the terms:
(-2 + 4y)(3 + y) = 0

Multiply (-2 + 4y) * (3 + y)
(-2(3 + y) + 4y * (3 + y)) = 0
((3 * -2 + y * -2) + 4y * (3 + y)) = 0
((-6 + -2y) + 4y * (3 + y)) = 0
(-6 + -2y + (3 * 4y + y * 4y)) = 0
(-6 + -2y + (12y + 4y2)) = 0

Combine like terms: -2y + 12y = 10y
(-6 + 10y + 4y2) = 0

Solving
-6 + 10y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5y + 2y2) = 0

Factor a trinomial.
2((-3 + -1y)(1 + -2y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
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 = {-3, 0.5}