6y+3(y+1)=y-2(y-3)+7

Solution for 6y+3(y+1)=y-2(y-3)+7 equation:

Simplifying
6y + 3(y + 1) = y + -2(y + -3) + 7

Reorder the terms:
6y + 3(1 + y) = y + -2(y + -3) + 7
6y + (1 * 3 + y * 3) = y + -2(y + -3) + 7
6y + (3 + 3y) = y + -2(y + -3) + 7

Reorder the terms:
3 + 6y + 3y = y + -2(y + -3) + 7

Combine like terms: 6y + 3y = 9y
3 + 9y = y + -2(y + -3) + 7

Reorder the terms:
3 + 9y = y + -2(-3 + y) + 7
3 + 9y = y + (-3 * -2 + y * -2) + 7
3 + 9y = y + (6 + -2y) + 7

Reorder the terms:
3 + 9y = 6 + 7 + y + -2y

Combine like terms: 6 + 7 = 13
3 + 9y = 13 + y + -2y

Combine like terms: y + -2y = -1y
3 + 9y = 13 + -1y

Solving
3 + 9y = 13 + -1y

Solving for variable 'y'.

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

Add 'y' to each side of the equation.
3 + 9y + y = 13 + -1y + y

Combine like terms: 9y + y = 10y
3 + 10y = 13 + -1y + y

Combine like terms: -1y + y = 0
3 + 10y = 13 + 0
3 + 10y = 13

Add '-3' to each side of the equation.
3 + -3 + 10y = 13 + -3

Combine like terms: 3 + -3 = 0
0 + 10y = 13 + -3
10y = 13 + -3

Combine like terms: 13 + -3 = 10
10y = 10

Divide each side by '10'.
y = 1

Simplifying
y = 1