10(y+4)-4(y-2)=3(y-1)+2(y-3)

Solution for 10(y+4)-4(y-2)=3(y-1)+2(y-3) equation:

Simplifying
10(y + 4) + -4(y + -2) = 3(y + -1) + 2(y + -3)

Reorder the terms:
10(4 + y) + -4(y + -2) = 3(y + -1) + 2(y + -3)
(4 * 10 + y * 10) + -4(y + -2) = 3(y + -1) + 2(y + -3)
(40 + 10y) + -4(y + -2) = 3(y + -1) + 2(y + -3)

Reorder the terms:
40 + 10y + -4(-2 + y) = 3(y + -1) + 2(y + -3)
40 + 10y + (-2 * -4 + y * -4) = 3(y + -1) + 2(y + -3)
40 + 10y + (8 + -4y) = 3(y + -1) + 2(y + -3)

Reorder the terms:
40 + 8 + 10y + -4y = 3(y + -1) + 2(y + -3)

Combine like terms: 40 + 8 = 48
48 + 10y + -4y = 3(y + -1) + 2(y + -3)

Combine like terms: 10y + -4y = 6y
48 + 6y = 3(y + -1) + 2(y + -3)

Reorder the terms:
48 + 6y = 3(-1 + y) + 2(y + -3)
48 + 6y = (-1 * 3 + y * 3) + 2(y + -3)
48 + 6y = (-3 + 3y) + 2(y + -3)

Reorder the terms:
48 + 6y = -3 + 3y + 2(-3 + y)
48 + 6y = -3 + 3y + (-3 * 2 + y * 2)
48 + 6y = -3 + 3y + (-6 + 2y)

Reorder the terms:
48 + 6y = -3 + -6 + 3y + 2y

Combine like terms: -3 + -6 = -9
48 + 6y = -9 + 3y + 2y

Combine like terms: 3y + 2y = 5y
48 + 6y = -9 + 5y

Solving
48 + 6y = -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.
48 + 6y + -5y = -9 + 5y + -5y

Combine like terms: 6y + -5y = 1y
48 + 1y = -9 + 5y + -5y

Combine like terms: 5y + -5y = 0
48 + 1y = -9 + 0
48 + 1y = -9

Add '-48' to each side of the equation.
48 + -48 + 1y = -9 + -48

Combine like terms: 48 + -48 = 0
0 + 1y = -9 + -48
1y = -9 + -48

Combine like terms: -9 + -48 = -57
1y = -57

Divide each side by '1'.
y = -57

Simplifying
y = -57