3(4-y)-5y+(y-2)(y+3)=y^2-9y+32

Solution for 3(4-y)-5y+(y-2)(y+3)=y^2-9y+32 equation:

Simplifying
3(4 + -1y) + -5y + (y + -2)(y + 3) = y2 + -9y + 32
(4 * 3 + -1y * 3) + -5y + (y + -2)(y + 3) = y2 + -9y + 32
(12 + -3y) + -5y + (y + -2)(y + 3) = y2 + -9y + 32

Reorder the terms:
12 + -3y + -5y + (-2 + y)(y + 3) = y2 + -9y + 32

Reorder the terms:
12 + -3y + -5y + (-2 + y)(3 + y) = y2 + -9y + 32

Multiply (-2 + y) * (3 + y)
12 + -3y + -5y + (-2(3 + y) + y(3 + y)) = y2 + -9y + 32
12 + -3y + -5y + ((3 * -2 + y * -2) + y(3 + y)) = y2 + -9y + 32
12 + -3y + -5y + ((-6 + -2y) + y(3 + y)) = y2 + -9y + 32
12 + -3y + -5y + (-6 + -2y + (3 * y + y * y)) = y2 + -9y + 32
12 + -3y + -5y + (-6 + -2y + (3y + y2)) = y2 + -9y + 32

Combine like terms: -2y + 3y = 1y
12 + -3y + -5y + (-6 + 1y + y2) = y2 + -9y + 32

Reorder the terms:
12 + -6 + -3y + -5y + 1y + y2 = y2 + -9y + 32

Combine like terms: 12 + -6 = 6
6 + -3y + -5y + 1y + y2 = y2 + -9y + 32

Combine like terms: -3y + -5y = -8y
6 + -8y + 1y + y2 = y2 + -9y + 32

Combine like terms: -8y + 1y = -7y
6 + -7y + y2 = y2 + -9y + 32

Reorder the terms:
6 + -7y + y2 = 32 + -9y + y2

Add '-1y2' to each side of the equation.
6 + -7y + y2 + -1y2 = 32 + -9y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + -7y + 0 = 32 + -9y + y2 + -1y2
6 + -7y = 32 + -9y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + -7y = 32 + -9y + 0
6 + -7y = 32 + -9y

Solving
6 + -7y = 32 + -9y

Solving for variable 'y'.

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

Add '9y' to each side of the equation.
6 + -7y + 9y = 32 + -9y + 9y

Combine like terms: -7y + 9y = 2y
6 + 2y = 32 + -9y + 9y

Combine like terms: -9y + 9y = 0
6 + 2y = 32 + 0
6 + 2y = 32

Add '-6' to each side of the equation.
6 + -6 + 2y = 32 + -6

Combine like terms: 6 + -6 = 0
0 + 2y = 32 + -6
2y = 32 + -6

Combine like terms: 32 + -6 = 26
2y = 26

Divide each side by '2'.
y = 13

Simplifying
y = 13