2(y+5)+6(y-5)=5y+1

Solution for 2(y+5)+6(y-5)=5y+1 equation:

Simplifying
2(y + 5) + 6(y + -5) = 5y + 1

Reorder the terms:
2(5 + y) + 6(y + -5) = 5y + 1
(5 * 2 + y * 2) + 6(y + -5) = 5y + 1
(10 + 2y) + 6(y + -5) = 5y + 1

Reorder the terms:
10 + 2y + 6(-5 + y) = 5y + 1
10 + 2y + (-5 * 6 + y * 6) = 5y + 1
10 + 2y + (-30 + 6y) = 5y + 1

Reorder the terms:
10 + -30 + 2y + 6y = 5y + 1

Combine like terms: 10 + -30 = -20
-20 + 2y + 6y = 5y + 1

Combine like terms: 2y + 6y = 8y
-20 + 8y = 5y + 1

Reorder the terms:
-20 + 8y = 1 + 5y

Solving
-20 + 8y = 1 + 5y

Solving for variable 'y'.

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

Add '-5y' to each side of the equation.
-20 + 8y + -5y = 1 + 5y + -5y

Combine like terms: 8y + -5y = 3y
-20 + 3y = 1 + 5y + -5y

Combine like terms: 5y + -5y = 0
-20 + 3y = 1 + 0
-20 + 3y = 1

Add '20' to each side of the equation.
-20 + 20 + 3y = 1 + 20

Combine like terms: -20 + 20 = 0
0 + 3y = 1 + 20
3y = 1 + 20

Combine like terms: 1 + 20 = 21
3y = 21

Divide each side by '3'.
y = 7

Simplifying
y = 7