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

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

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

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

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

Solving
-6 + 2y = -15 + 3y

Solving for variable 'y'.

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

Add '-3y' to each side of the equation.
-6 + 2y + -3y = -15 + 3y + -3y

Combine like terms: 2y + -3y = -1y
-6 + -1y = -15 + 3y + -3y

Combine like terms: 3y + -3y = 0
-6 + -1y = -15 + 0
-6 + -1y = -15

Add '6' to each side of the equation.
-6 + 6 + -1y = -15 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = -15 + 6
-1y = -15 + 6

Combine like terms: -15 + 6 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9