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

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

Simplifying
4y + 3(2y + 4) = 2(2y + 4) * y

Reorder the terms:
4y + 3(4 + 2y) = 2(2y + 4) * y
4y + (4 * 3 + 2y * 3) = 2(2y + 4) * y
4y + (12 + 6y) = 2(2y + 4) * y

Reorder the terms:
12 + 4y + 6y = 2(2y + 4) * y

Combine like terms: 4y + 6y = 10y
12 + 10y = 2(2y + 4) * y

Reorder the terms:
12 + 10y = 2(4 + 2y) * y

Reorder the terms for easier multiplication:
12 + 10y = 2y(4 + 2y)
12 + 10y = (4 * 2y + 2y * 2y)
12 + 10y = (8y + 4y2)

Solving
12 + 10y = 8y + 4y2

Solving for variable 'y'.

Combine like terms: 10y + -8y = 2y
12 + 2y + -4y2 = 8y + 4y2 + -8y + -4y2

Reorder the terms:
12 + 2y + -4y2 = 8y + -8y + 4y2 + -4y2

Combine like terms: 8y + -8y = 0
12 + 2y + -4y2 = 0 + 4y2 + -4y2
12 + 2y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
12 + 2y + -4y2 = 0

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

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

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

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

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Subproblem 2
Set the factor '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 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 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {2, -1.5}