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

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

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

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

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

Solving
-6 + 2y = 15 + 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 = 15 + 5y + -5y

Combine like terms: 2y + -5y = -3y
-6 + -3y = 15 + 5y + -5y

Combine like terms: 5y + -5y = 0
-6 + -3y = 15 + 0
-6 + -3y = 15

Add '6' to each side of the equation.
-6 + 6 + -3y = 15 + 6

Combine like terms: -6 + 6 = 0
0 + -3y = 15 + 6
-3y = 15 + 6

Combine like terms: 15 + 6 = 21
-3y = 21

Divide each side by '-3'.
y = -7

Simplifying
y = -7