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

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

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

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

Reorder the terms:
3 + 5y = 3(-3 + y) + -2(y + 2)
3 + 5y = (-3 * 3 + y * 3) + -2(y + 2)
3 + 5y = (-9 + 3y) + -2(y + 2)

Reorder the terms:
3 + 5y = -9 + 3y + -2(2 + y)
3 + 5y = -9 + 3y + (2 * -2 + y * -2)
3 + 5y = -9 + 3y + (-4 + -2y)

Reorder the terms:
3 + 5y = -9 + -4 + 3y + -2y

Combine like terms: -9 + -4 = -13
3 + 5y = -13 + 3y + -2y

Combine like terms: 3y + -2y = 1y
3 + 5y = -13 + 1y

Solving
3 + 5y = -13 + 1y

Solving for variable 'y'.

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

Add '-1y' to each side of the equation.
3 + 5y + -1y = -13 + 1y + -1y

Combine like terms: 5y + -1y = 4y
3 + 4y = -13 + 1y + -1y

Combine like terms: 1y + -1y = 0
3 + 4y = -13 + 0
3 + 4y = -13

Add '-3' to each side of the equation.
3 + -3 + 4y = -13 + -3

Combine like terms: 3 + -3 = 0
0 + 4y = -13 + -3
4y = -13 + -3

Combine like terms: -13 + -3 = -16
4y = -16

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

Simplifying
y = -4