2(y+3)+3(y+5)=4y-32

Solution for 2(y+3)+3(y+5)=4y-32 equation:

Simplifying
2(y + 3) + 3(y + 5) = 4y + -32

Reorder the terms:
2(3 + y) + 3(y + 5) = 4y + -32
(3 * 2 + y * 2) + 3(y + 5) = 4y + -32
(6 + 2y) + 3(y + 5) = 4y + -32

Reorder the terms:
6 + 2y + 3(5 + y) = 4y + -32
6 + 2y + (5 * 3 + y * 3) = 4y + -32
6 + 2y + (15 + 3y) = 4y + -32

Reorder the terms:
6 + 15 + 2y + 3y = 4y + -32

Combine like terms: 6 + 15 = 21
21 + 2y + 3y = 4y + -32

Combine like terms: 2y + 3y = 5y
21 + 5y = 4y + -32

Reorder the terms:
21 + 5y = -32 + 4y

Solving
21 + 5y = -32 + 4y

Solving for variable 'y'.

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

Add '-4y' to each side of the equation.
21 + 5y + -4y = -32 + 4y + -4y

Combine like terms: 5y + -4y = 1y
21 + 1y = -32 + 4y + -4y

Combine like terms: 4y + -4y = 0
21 + 1y = -32 + 0
21 + 1y = -32

Add '-21' to each side of the equation.
21 + -21 + 1y = -32 + -21

Combine like terms: 21 + -21 = 0
0 + 1y = -32 + -21
1y = -32 + -21

Combine like terms: -32 + -21 = -53
1y = -53

Divide each side by '1'.
y = -53

Simplifying
y = -53