(2x+6y)(3x+1y)=(6x+2y)(1x+3y)

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Solution for (2x+6y)(3x+1y)=(6x+2y)(1x+3y) equation: 


Simplifying
(2x + 6y)(3x + 1y) = (6x + 2y)(1x + 3y)

Multiply (2x + 6y) * (3x + 1y)
(2x * (3x + 1y) + 6y * (3x + 1y)) = (6x + 2y)(1x + 3y)
((3x * 2x + 1y * 2x) + 6y * (3x + 1y)) = (6x + 2y)(1x + 3y)

Reorder the terms:
((2xy + 6x2) + 6y * (3x + 1y)) = (6x + 2y)(1x + 3y)
((2xy + 6x2) + 6y * (3x + 1y)) = (6x + 2y)(1x + 3y)
(2xy + 6x2 + (3x * 6y + 1y * 6y)) = (6x + 2y)(1x + 3y)
(2xy + 6x2 + (18xy + 6y2)) = (6x + 2y)(1x + 3y)

Reorder the terms:
(2xy + 18xy + 6x2 + 6y2) = (6x + 2y)(1x + 3y)

Combine like terms: 2xy + 18xy = 20xy
(20xy + 6x2 + 6y2) = (6x + 2y)(1x + 3y)

Multiply (6x + 2y) * (1x + 3y)
20xy + 6x2 + 6y2 = (6x * (1x + 3y) + 2y * (1x + 3y))
20xy + 6x2 + 6y2 = ((1x * 6x + 3y * 6x) + 2y * (1x + 3y))

Reorder the terms:
20xy + 6x2 + 6y2 = ((18xy + 6x2) + 2y * (1x + 3y))
20xy + 6x2 + 6y2 = ((18xy + 6x2) + 2y * (1x + 3y))
20xy + 6x2 + 6y2 = (18xy + 6x2 + (1x * 2y + 3y * 2y))
20xy + 6x2 + 6y2 = (18xy + 6x2 + (2xy + 6y2))

Reorder the terms:
20xy + 6x2 + 6y2 = (18xy + 2xy + 6x2 + 6y2)

Combine like terms: 18xy + 2xy = 20xy
20xy + 6x2 + 6y2 = (20xy + 6x2 + 6y2)

Add '-20xy' to each side of the equation.
20xy + 6x2 + -20xy + 6y2 = 20xy + 6x2 + -20xy + 6y2

Reorder the terms:
20xy + -20xy + 6x2 + 6y2 = 20xy + 6x2 + -20xy + 6y2

Combine like terms: 20xy + -20xy = 0
0 + 6x2 + 6y2 = 20xy + 6x2 + -20xy + 6y2
6x2 + 6y2 = 20xy + 6x2 + -20xy + 6y2

Reorder the terms:
6x2 + 6y2 = 20xy + -20xy + 6x2 + 6y2

Combine like terms: 20xy + -20xy = 0
6x2 + 6y2 = 0 + 6x2 + 6y2
6x2 + 6y2 = 6x2 + 6y2

Add '-6x2' to each side of the equation.
6x2 + -6x2 + 6y2 = 6x2 + -6x2 + 6y2

Combine like terms: 6x2 + -6x2 = 0
0 + 6y2 = 6x2 + -6x2 + 6y2
6y2 = 6x2 + -6x2 + 6y2

Combine like terms: 6x2 + -6x2 = 0
6y2 = 0 + 6y2
6y2 = 6y2

Add '-6y2' to each side of the equation.
6y2 + -6y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
0 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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