(8+y)(y-3)=(6+y)(y-4)

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Solution for (8+y)(y-3)=(6+y)(y-4) equation: 


Simplifying
(8 + y)(y + -3) = (6 + y)(y + -4)

Reorder the terms:
(8 + y)(-3 + y) = (6 + y)(y + -4)

Multiply (8 + y) * (-3 + y)
(8(-3 + y) + y(-3 + y)) = (6 + y)(y + -4)
((-3 * 8 + y * 8) + y(-3 + y)) = (6 + y)(y + -4)
((-24 + 8y) + y(-3 + y)) = (6 + y)(y + -4)
(-24 + 8y + (-3 * y + y * y)) = (6 + y)(y + -4)
(-24 + 8y + (-3y + y2)) = (6 + y)(y + -4)

Combine like terms: 8y + -3y = 5y
(-24 + 5y + y2) = (6 + y)(y + -4)

Reorder the terms:
-24 + 5y + y2 = (6 + y)(-4 + y)

Multiply (6 + y) * (-4 + y)
-24 + 5y + y2 = (6(-4 + y) + y(-4 + y))
-24 + 5y + y2 = ((-4 * 6 + y * 6) + y(-4 + y))
-24 + 5y + y2 = ((-24 + 6y) + y(-4 + y))
-24 + 5y + y2 = (-24 + 6y + (-4 * y + y * y))
-24 + 5y + y2 = (-24 + 6y + (-4y + y2))

Combine like terms: 6y + -4y = 2y
-24 + 5y + y2 = (-24 + 2y + y2)

Add '24' to each side of the equation.
-24 + 5y + 24 + y2 = -24 + 2y + 24 + y2

Reorder the terms:
-24 + 24 + 5y + y2 = -24 + 2y + 24 + y2

Combine like terms: -24 + 24 = 0
0 + 5y + y2 = -24 + 2y + 24 + y2
5y + y2 = -24 + 2y + 24 + y2

Reorder the terms:
5y + y2 = -24 + 24 + 2y + y2

Combine like terms: -24 + 24 = 0
5y + y2 = 0 + 2y + y2
5y + y2 = 2y + y2

Add '-1y2' to each side of the equation.
5y + y2 + -1y2 = 2y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
5y + 0 = 2y + y2 + -1y2
5y = 2y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
5y = 2y + 0
5y = 2y

Solving
5y = 2y

Solving for variable 'y'.

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

Add '-2y' to each side of the equation.
5y + -2y = 2y + -2y

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

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

Divide each side by '3'.
y = 0

Simplifying
y = 0

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