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

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

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

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

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

Combine like terms: y + -2y = -1y
2 + -1y = 3(y + -2)

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

Solving
2 + -1y = -6 + 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.
2 + -1y + -3y = -6 + 3y + -3y

Combine like terms: -1y + -3y = -4y
2 + -4y = -6 + 3y + -3y

Combine like terms: 3y + -3y = 0
2 + -4y = -6 + 0
2 + -4y = -6

Add '-2' to each side of the equation.
2 + -2 + -4y = -6 + -2

Combine like terms: 2 + -2 = 0
0 + -4y = -6 + -2
-4y = -6 + -2

Combine like terms: -6 + -2 = -8
-4y = -8

Divide each side by '-4'.
y = 2

Simplifying
y = 2