y+2(y+3)+3(y+1)=45

Solution for y+2(y+3)+3(y+1)=45 equation:

Simplifying
y + 2(y + 3) + 3(y + 1) = 45

Reorder the terms:
y + 2(3 + y) + 3(y + 1) = 45
y + (3 * 2 + y * 2) + 3(y + 1) = 45
y + (6 + 2y) + 3(y + 1) = 45

Reorder the terms:
y + 6 + 2y + 3(1 + y) = 45
y + 6 + 2y + (1 * 3 + y * 3) = 45
y + 6 + 2y + (3 + 3y) = 45

Reorder the terms:
6 + 3 + y + 2y + 3y = 45

Combine like terms: 6 + 3 = 9
9 + y + 2y + 3y = 45

Combine like terms: y + 2y = 3y
9 + 3y + 3y = 45

Combine like terms: 3y + 3y = 6y
9 + 6y = 45

Solving
9 + 6y = 45

Solving for variable 'y'.

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

Add '-9' to each side of the equation.
9 + -9 + 6y = 45 + -9

Combine like terms: 9 + -9 = 0
0 + 6y = 45 + -9
6y = 45 + -9

Combine like terms: 45 + -9 = 36
6y = 36

Divide each side by '6'.
y = 6

Simplifying
y = 6