(5x+8)(17y+3)=(21x)(20y-2)

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Solution for (5x+8)(17y+3)=(21x)(20y-2) equation:


Simplifying
(5x + 8)(17y + 3) = (21x)(20y + -2)

Reorder the terms:
(8 + 5x)(17y + 3) = (21x)(20y + -2)

Reorder the terms:
(8 + 5x)(3 + 17y) = (21x)(20y + -2)

Multiply (8 + 5x) * (3 + 17y)
(8(3 + 17y) + 5x * (3 + 17y)) = (21x)(20y + -2)
((3 * 8 + 17y * 8) + 5x * (3 + 17y)) = (21x)(20y + -2)
((24 + 136y) + 5x * (3 + 17y)) = (21x)(20y + -2)
(24 + 136y + (3 * 5x + 17y * 5x)) = (21x)(20y + -2)
(24 + 136y + (15x + 85xy)) = (21x)(20y + -2)

Reorder the terms:
(24 + 15x + 85xy + 136y) = (21x)(20y + -2)
(24 + 15x + 85xy + 136y) = (21x)(20y + -2)

Remove parenthesis around (21x)
24 + 15x + 85xy + 136y = 21x(20y + -2)

Reorder the terms:
24 + 15x + 85xy + 136y = 21x(-2 + 20y)
24 + 15x + 85xy + 136y = (-2 * 21x + 20y * 21x)
24 + 15x + 85xy + 136y = (-42x + 420xy)

Solving
24 + 15x + 85xy + 136y = -42x + 420xy

Solving for variable 'x'.

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

Add '42x' to each side of the equation.
24 + 15x + 85xy + 42x + 136y = -42x + 42x + 420xy

Reorder the terms:
24 + 15x + 42x + 85xy + 136y = -42x + 42x + 420xy

Combine like terms: 15x + 42x = 57x
24 + 57x + 85xy + 136y = -42x + 42x + 420xy

Combine like terms: -42x + 42x = 0
24 + 57x + 85xy + 136y = 0 + 420xy
24 + 57x + 85xy + 136y = 420xy

Add '-420xy' to each side of the equation.
24 + 57x + 85xy + -420xy + 136y = 420xy + -420xy

Combine like terms: 85xy + -420xy = -335xy
24 + 57x + -335xy + 136y = 420xy + -420xy

Combine like terms: 420xy + -420xy = 0
24 + 57x + -335xy + 136y = 0

Add '-24' to each side of the equation.
24 + 57x + -335xy + -24 + 136y = 0 + -24

Reorder the terms:
24 + -24 + 57x + -335xy + 136y = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 57x + -335xy + 136y = 0 + -24
57x + -335xy + 136y = 0 + -24

Combine like terms: 0 + -24 = -24
57x + -335xy + 136y = -24

Add '-136y' to each side of the equation.
57x + -335xy + 136y + -136y = -24 + -136y

Combine like terms: 136y + -136y = 0
57x + -335xy + 0 = -24 + -136y
57x + -335xy = -24 + -136y

Reorder the terms:
24 + 57x + -335xy + 136y = -24 + -136y + 24 + 136y

Reorder the terms:
24 + 57x + -335xy + 136y = -24 + 24 + -136y + 136y

Combine like terms: -24 + 24 = 0
24 + 57x + -335xy + 136y = 0 + -136y + 136y
24 + 57x + -335xy + 136y = -136y + 136y

Combine like terms: -136y + 136y = 0
24 + 57x + -335xy + 136y = 0

The solution to this equation could not be determined.

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