6y+3(y+5)-7(y+3)=6y-9+2(y+5)

Solution for 6y+3(y+5)-7(y+3)=6y-9+2(y+5) equation:

Simplifying
6y + 3(y + 5) + -7(y + 3) = 6y + -9 + 2(y + 5)

Reorder the terms:
6y + 3(5 + y) + -7(y + 3) = 6y + -9 + 2(y + 5)
6y + (5 * 3 + y * 3) + -7(y + 3) = 6y + -9 + 2(y + 5)
6y + (15 + 3y) + -7(y + 3) = 6y + -9 + 2(y + 5)

Reorder the terms:
6y + 15 + 3y + -7(3 + y) = 6y + -9 + 2(y + 5)
6y + 15 + 3y + (3 * -7 + y * -7) = 6y + -9 + 2(y + 5)
6y + 15 + 3y + (-21 + -7y) = 6y + -9 + 2(y + 5)

Reorder the terms:
15 + -21 + 6y + 3y + -7y = 6y + -9 + 2(y + 5)

Combine like terms: 15 + -21 = -6
-6 + 6y + 3y + -7y = 6y + -9 + 2(y + 5)

Combine like terms: 6y + 3y = 9y
-6 + 9y + -7y = 6y + -9 + 2(y + 5)

Combine like terms: 9y + -7y = 2y
-6 + 2y = 6y + -9 + 2(y + 5)

Reorder the terms:
-6 + 2y = 6y + -9 + 2(5 + y)
-6 + 2y = 6y + -9 + (5 * 2 + y * 2)
-6 + 2y = 6y + -9 + (10 + 2y)

Reorder the terms:
-6 + 2y = -9 + 10 + 6y + 2y

Combine like terms: -9 + 10 = 1
-6 + 2y = 1 + 6y + 2y

Combine like terms: 6y + 2y = 8y
-6 + 2y = 1 + 8y

Solving
-6 + 2y = 1 + 8y

Solving for variable 'y'.

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

Add '-8y' to each side of the equation.
-6 + 2y + -8y = 1 + 8y + -8y

Combine like terms: 2y + -8y = -6y
-6 + -6y = 1 + 8y + -8y

Combine like terms: 8y + -8y = 0
-6 + -6y = 1 + 0
-6 + -6y = 1

Add '6' to each side of the equation.
-6 + 6 + -6y = 1 + 6

Combine like terms: -6 + 6 = 0
0 + -6y = 1 + 6
-6y = 1 + 6

Combine like terms: 1 + 6 = 7
-6y = 7

Divide each side by '-6'.
y = -1.166666667

Simplifying
y = -1.166666667