(x+10)(y-40)=(x-5)(y+50)

Solution for (x+10)(y-40)=(x-5)(y+50) equation:

Simplifying
(x + 10)(y + -40) = (x + -5)(y + 50)

Reorder the terms:
(10 + x)(y + -40) = (x + -5)(y + 50)

Reorder the terms:
(10 + x)(-40 + y) = (x + -5)(y + 50)

Multiply (10 + x) * (-40 + y)
(10(-40 + y) + x(-40 + y)) = (x + -5)(y + 50)
((-40 * 10 + y * 10) + x(-40 + y)) = (x + -5)(y + 50)
((-400 + 10y) + x(-40 + y)) = (x + -5)(y + 50)
(-400 + 10y + (-40 * x + y * x)) = (x + -5)(y + 50)
(-400 + 10y + (-40x + xy)) = (x + -5)(y + 50)

Reorder the terms:
(-400 + -40x + xy + 10y) = (x + -5)(y + 50)
(-400 + -40x + xy + 10y) = (x + -5)(y + 50)

Reorder the terms:
-400 + -40x + xy + 10y = (-5 + x)(y + 50)

Reorder the terms:
-400 + -40x + xy + 10y = (-5 + x)(50 + y)

Multiply (-5 + x) * (50 + y)
-400 + -40x + xy + 10y = (-5(50 + y) + x(50 + y))
-400 + -40x + xy + 10y = ((50 * -5 + y * -5) + x(50 + y))
-400 + -40x + xy + 10y = ((-250 + -5y) + x(50 + y))
-400 + -40x + xy + 10y = (-250 + -5y + (50 * x + y * x))
-400 + -40x + xy + 10y = (-250 + -5y + (50x + xy))

Reorder the terms:
-400 + -40x + xy + 10y = (-250 + 50x + xy + -5y)
-400 + -40x + xy + 10y = (-250 + 50x + xy + -5y)

Add '-1xy' to each side of the equation.
-400 + -40x + xy + -1xy + 10y = -250 + 50x + xy + -1xy + -5y

Combine like terms: xy + -1xy = 0
-400 + -40x + 0 + 10y = -250 + 50x + xy + -1xy + -5y
-400 + -40x + 10y = -250 + 50x + xy + -1xy + -5y

Combine like terms: xy + -1xy = 0
-400 + -40x + 10y = -250 + 50x + 0 + -5y
-400 + -40x + 10y = -250 + 50x + -5y

Solving
-400 + -40x + 10y = -250 + 50x + -5y

Solving for variable 'x'.

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

Add '-50x' to each side of the equation.
-400 + -40x + -50x + 10y = -250 + 50x + -50x + -5y

Combine like terms: -40x + -50x = -90x
-400 + -90x + 10y = -250 + 50x + -50x + -5y

Combine like terms: 50x + -50x = 0
-400 + -90x + 10y = -250 + 0 + -5y
-400 + -90x + 10y = -250 + -5y

Add '400' to each side of the equation.
-400 + -90x + 400 + 10y = -250 + 400 + -5y

Reorder the terms:
-400 + 400 + -90x + 10y = -250 + 400 + -5y

Combine like terms: -400 + 400 = 0
0 + -90x + 10y = -250 + 400 + -5y
-90x + 10y = -250 + 400 + -5y

Combine like terms: -250 + 400 = 150
-90x + 10y = 150 + -5y

Add '-10y' to each side of the equation.
-90x + 10y + -10y = 150 + -5y + -10y

Combine like terms: 10y + -10y = 0
-90x + 0 = 150 + -5y + -10y
-90x = 150 + -5y + -10y

Combine like terms: -5y + -10y = -15y
-90x = 150 + -15y

Divide each side by '-90'.
x = -1.666666667 + 0.1666666667y

Simplifying
x = -1.666666667 + 0.1666666667y