(y+12)(y-3)=y(y+5)+24

Solution for (y+12)(y-3)=y(y+5)+24 equation:

Simplifying
(y + 12)(y + -3) = y(y + 5) + 24

Reorder the terms:
(12 + y)(y + -3) = y(y + 5) + 24

Reorder the terms:
(12 + y)(-3 + y) = y(y + 5) + 24

Multiply (12 + y) * (-3 + y)
(12(-3 + y) + y(-3 + y)) = y(y + 5) + 24
((-3 * 12 + y * 12) + y(-3 + y)) = y(y + 5) + 24
((-36 + 12y) + y(-3 + y)) = y(y + 5) + 24
(-36 + 12y + (-3 * y + y * y)) = y(y + 5) + 24
(-36 + 12y + (-3y + y2)) = y(y + 5) + 24

Combine like terms: 12y + -3y = 9y
(-36 + 9y + y2) = y(y + 5) + 24

Reorder the terms:
-36 + 9y + y2 = y(5 + y) + 24
-36 + 9y + y2 = (5 * y + y * y) + 24
-36 + 9y + y2 = (5y + y2) + 24

Reorder the terms:
-36 + 9y + y2 = 24 + 5y + y2

Add '-1y2' to each side of the equation.
-36 + 9y + y2 + -1y2 = 24 + 5y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-36 + 9y + 0 = 24 + 5y + y2 + -1y2
-36 + 9y = 24 + 5y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-36 + 9y = 24 + 5y + 0
-36 + 9y = 24 + 5y

Solving
-36 + 9y = 24 + 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.
-36 + 9y + -5y = 24 + 5y + -5y

Combine like terms: 9y + -5y = 4y
-36 + 4y = 24 + 5y + -5y

Combine like terms: 5y + -5y = 0
-36 + 4y = 24 + 0
-36 + 4y = 24

Add '36' to each side of the equation.
-36 + 36 + 4y = 24 + 36

Combine like terms: -36 + 36 = 0
0 + 4y = 24 + 36
4y = 24 + 36

Combine like terms: 24 + 36 = 60
4y = 60

Divide each side by '4'.
y = 15

Simplifying
y = 15