2(y+3)=5(y-2)+1

Solution for 2(y+3)=5(y-2)+1 equation:

Simplifying
2(y + 3) = 5(y + -2) + 1

Reorder the terms:
2(3 + y) = 5(y + -2) + 1
(3 * 2 + y * 2) = 5(y + -2) + 1
(6 + 2y) = 5(y + -2) + 1

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

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

Combine like terms: -10 + 1 = -9
6 + 2y = -9 + 5y

Solving
6 + 2y = -9 + 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.
6 + 2y + -5y = -9 + 5y + -5y

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

Combine like terms: 5y + -5y = 0
6 + -3y = -9 + 0
6 + -3y = -9

Add '-6' to each side of the equation.
6 + -6 + -3y = -9 + -6

Combine like terms: 6 + -6 = 0
0 + -3y = -9 + -6
-3y = -9 + -6

Combine like terms: -9 + -6 = -15
-3y = -15

Divide each side by '-3'.
y = 5

Simplifying
y = 5