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

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

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

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

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

Combine like terms: 1 + -3 = -2
6 + 2y = -2 + -6y

Solving
6 + 2y = -2 + -6y

Solving for variable 'y'.

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

Add '6y' to each side of the equation.
6 + 2y + 6y = -2 + -6y + 6y

Combine like terms: 2y + 6y = 8y
6 + 8y = -2 + -6y + 6y

Combine like terms: -6y + 6y = 0
6 + 8y = -2 + 0
6 + 8y = -2

Add '-6' to each side of the equation.
6 + -6 + 8y = -2 + -6

Combine like terms: 6 + -6 = 0
0 + 8y = -2 + -6
8y = -2 + -6

Combine like terms: -2 + -6 = -8
8y = -8

Divide each side by '8'.
y = -1

Simplifying
y = -1