(y-1000)(x+3)=(y+1000)(x-2)

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Solution for (y-1000)(x+3)=(y+1000)(x-2) equation: 


Simplifying
(y + -1000)(x + 3) = (y + 1000)(x + -2)

Reorder the terms:
(-1000 + y)(x + 3) = (y + 1000)(x + -2)

Reorder the terms:
(-1000 + y)(3 + x) = (y + 1000)(x + -2)

Multiply (-1000 + y) * (3 + x)
(-1000(3 + x) + y(3 + x)) = (y + 1000)(x + -2)
((3 * -1000 + x * -1000) + y(3 + x)) = (y + 1000)(x + -2)
((-3000 + -1000x) + y(3 + x)) = (y + 1000)(x + -2)
(-3000 + -1000x + (3 * y + x * y)) = (y + 1000)(x + -2)

Reorder the terms:
(-3000 + -1000x + (xy + 3y)) = (y + 1000)(x + -2)
(-3000 + -1000x + (xy + 3y)) = (y + 1000)(x + -2)
(-3000 + -1000x + xy + 3y) = (y + 1000)(x + -2)

Reorder the terms:
-3000 + -1000x + xy + 3y = (1000 + y)(x + -2)

Reorder the terms:
-3000 + -1000x + xy + 3y = (1000 + y)(-2 + x)

Multiply (1000 + y) * (-2 + x)
-3000 + -1000x + xy + 3y = (1000(-2 + x) + y(-2 + x))
-3000 + -1000x + xy + 3y = ((-2 * 1000 + x * 1000) + y(-2 + x))
-3000 + -1000x + xy + 3y = ((-2000 + 1000x) + y(-2 + x))
-3000 + -1000x + xy + 3y = (-2000 + 1000x + (-2 * y + x * y))

Reorder the terms:
-3000 + -1000x + xy + 3y = (-2000 + 1000x + (xy + -2y))
-3000 + -1000x + xy + 3y = (-2000 + 1000x + (xy + -2y))
-3000 + -1000x + xy + 3y = (-2000 + 1000x + xy + -2y)

Add '-1xy' to each side of the equation.
-3000 + -1000x + xy + -1xy + 3y = -2000 + 1000x + xy + -1xy + -2y

Combine like terms: xy + -1xy = 0
-3000 + -1000x + 0 + 3y = -2000 + 1000x + xy + -1xy + -2y
-3000 + -1000x + 3y = -2000 + 1000x + xy + -1xy + -2y

Combine like terms: xy + -1xy = 0
-3000 + -1000x + 3y = -2000 + 1000x + 0 + -2y
-3000 + -1000x + 3y = -2000 + 1000x + -2y

Solving
-3000 + -1000x + 3y = -2000 + 1000x + -2y

Solving for variable 'x'.

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

Add '-1000x' to each side of the equation.
-3000 + -1000x + -1000x + 3y = -2000 + 1000x + -1000x + -2y

Combine like terms: -1000x + -1000x = -2000x
-3000 + -2000x + 3y = -2000 + 1000x + -1000x + -2y

Combine like terms: 1000x + -1000x = 0
-3000 + -2000x + 3y = -2000 + 0 + -2y
-3000 + -2000x + 3y = -2000 + -2y

Add '3000' to each side of the equation.
-3000 + -2000x + 3000 + 3y = -2000 + 3000 + -2y

Reorder the terms:
-3000 + 3000 + -2000x + 3y = -2000 + 3000 + -2y

Combine like terms: -3000 + 3000 = 0
0 + -2000x + 3y = -2000 + 3000 + -2y
-2000x + 3y = -2000 + 3000 + -2y

Combine like terms: -2000 + 3000 = 1000
-2000x + 3y = 1000 + -2y

Add '-3y' to each side of the equation.
-2000x + 3y + -3y = 1000 + -2y + -3y

Combine like terms: 3y + -3y = 0
-2000x + 0 = 1000 + -2y + -3y
-2000x = 1000 + -2y + -3y

Combine like terms: -2y + -3y = -5y
-2000x = 1000 + -5y

Divide each side by '-2000'.
x = -0.5 + 0.0025y

Simplifying
x = -0.5 + 0.0025y

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