(x+10)(y-0.40)=(x-5)(y+0.50)

Solution for (x+10)(y-0.40)=(x-5)(y+0.50) equation:

Simplifying
(x + 10)(y + -0.40) = (x + -5)(y + 0.50)

Reorder the terms:
(10 + x)(y + -0.40) = (x + -5)(y + 0.50)

Reorder the terms:
(10 + x)(-0.40 + y) = (x + -5)(y + 0.50)

Multiply (10 + x) * (-0.40 + y)
(10(-0.40 + y) + x(-0.40 + y)) = (x + -5)(y + 0.50)
((-0.40 * 10 + y * 10) + x(-0.40 + y)) = (x + -5)(y + 0.50)
((-4 + 10y) + x(-0.40 + y)) = (x + -5)(y + 0.50)
(-4 + 10y + (-0.40 * x + y * x)) = (x + -5)(y + 0.50)
(-4 + 10y + (-0.40x + xy)) = (x + -5)(y + 0.50)

Reorder the terms:
(-4 + -0.40x + xy + 10y) = (x + -5)(y + 0.50)
(-4 + -0.40x + xy + 10y) = (x + -5)(y + 0.50)

Reorder the terms:
-4 + -0.40x + xy + 10y = (-5 + x)(y + 0.50)

Reorder the terms:
-4 + -0.40x + xy + 10y = (-5 + x)(0.50 + y)

Multiply (-5 + x) * (0.50 + y)
-4 + -0.40x + xy + 10y = (-5(0.50 + y) + x(0.50 + y))
-4 + -0.40x + xy + 10y = ((0.50 * -5 + y * -5) + x(0.50 + y))
-4 + -0.40x + xy + 10y = ((-2.5 + -5y) + x(0.50 + y))
-4 + -0.40x + xy + 10y = (-2.5 + -5y + (0.50 * x + y * x))
-4 + -0.40x + xy + 10y = (-2.5 + -5y + (0.50x + xy))

Reorder the terms:
-4 + -0.40x + xy + 10y = (-2.5 + 0.50x + xy + -5y)
-4 + -0.40x + xy + 10y = (-2.5 + 0.50x + xy + -5y)

Add '-1xy' to each side of the equation.
-4 + -0.40x + xy + -1xy + 10y = -2.5 + 0.50x + xy + -1xy + -5y

Combine like terms: xy + -1xy = 0
-4 + -0.40x + 0 + 10y = -2.5 + 0.50x + xy + -1xy + -5y
-4 + -0.40x + 10y = -2.5 + 0.50x + xy + -1xy + -5y

Combine like terms: xy + -1xy = 0
-4 + -0.40x + 10y = -2.5 + 0.50x + 0 + -5y
-4 + -0.40x + 10y = -2.5 + 0.50x + -5y

Solving
-4 + -0.40x + 10y = -2.5 + 0.50x + -5y

Solving for variable 'x'.

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

Add '-0.50x' to each side of the equation.
-4 + -0.40x + -0.50x + 10y = -2.5 + 0.50x + -0.50x + -5y

Combine like terms: -0.40x + -0.50x = -0.9x
-4 + -0.9x + 10y = -2.5 + 0.50x + -0.50x + -5y

Combine like terms: 0.50x + -0.50x = 0.00
-4 + -0.9x + 10y = -2.5 + 0.00 + -5y
-4 + -0.9x + 10y = -2.5 + -5y

Add '4' to each side of the equation.
-4 + -0.9x + 4 + 10y = -2.5 + 4 + -5y

Reorder the terms:
-4 + 4 + -0.9x + 10y = -2.5 + 4 + -5y

Combine like terms: -4 + 4 = 0
0 + -0.9x + 10y = -2.5 + 4 + -5y
-0.9x + 10y = -2.5 + 4 + -5y

Combine like terms: -2.5 + 4 = 1.5
-0.9x + 10y = 1.5 + -5y

Add '-10y' to each side of the equation.
-0.9x + 10y + -10y = 1.5 + -5y + -10y

Combine like terms: 10y + -10y = 0
-0.9x + 0 = 1.5 + -5y + -10y
-0.9x = 1.5 + -5y + -10y

Combine like terms: -5y + -10y = -15y
-0.9x = 1.5 + -15y

Divide each side by '-0.9'.
x = -1.666666667 + 16.66666667y

Simplifying
x = -1.666666667 + 16.66666667y