(4x+3)(3x+1)=(4x-y)(x+6y)

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Solution for (4x+3)(3x+1)=(4x-y)(x+6y) equation: 


Simplifying
(4x + 3)(3x + 1) = (4x + -1y)(x + 6y)

Reorder the terms:
(3 + 4x)(3x + 1) = (4x + -1y)(x + 6y)

Reorder the terms:
(3 + 4x)(1 + 3x) = (4x + -1y)(x + 6y)

Multiply (3 + 4x) * (1 + 3x)
(3(1 + 3x) + 4x * (1 + 3x)) = (4x + -1y)(x + 6y)
((1 * 3 + 3x * 3) + 4x * (1 + 3x)) = (4x + -1y)(x + 6y)
((3 + 9x) + 4x * (1 + 3x)) = (4x + -1y)(x + 6y)
(3 + 9x + (1 * 4x + 3x * 4x)) = (4x + -1y)(x + 6y)
(3 + 9x + (4x + 12x2)) = (4x + -1y)(x + 6y)

Combine like terms: 9x + 4x = 13x
(3 + 13x + 12x2) = (4x + -1y)(x + 6y)

Multiply (4x + -1y) * (x + 6y)
3 + 13x + 12x2 = (4x * (x + 6y) + -1y * (x + 6y))
3 + 13x + 12x2 = ((x * 4x + 6y * 4x) + -1y * (x + 6y))

Reorder the terms:
3 + 13x + 12x2 = ((24xy + 4x2) + -1y * (x + 6y))
3 + 13x + 12x2 = ((24xy + 4x2) + -1y * (x + 6y))
3 + 13x + 12x2 = (24xy + 4x2 + (x * -1y + 6y * -1y))
3 + 13x + 12x2 = (24xy + 4x2 + (-1xy + -6y2))

Reorder the terms:
3 + 13x + 12x2 = (24xy + -1xy + 4x2 + -6y2)

Combine like terms: 24xy + -1xy = 23xy
3 + 13x + 12x2 = (23xy + 4x2 + -6y2)

Solving
3 + 13x + 12x2 = 23xy + 4x2 + -6y2

Solving for variable 'x'.

Reorder the terms:
3 + 13x + -23xy + 12x2 + -4x2 + 6y2 = 23xy + 4x2 + -6y2 + -23xy + -4x2 + 6y2

Combine like terms: 12x2 + -4x2 = 8x2
3 + 13x + -23xy + 8x2 + 6y2 = 23xy + 4x2 + -6y2 + -23xy + -4x2 + 6y2

Reorder the terms:
3 + 13x + -23xy + 8x2 + 6y2 = 23xy + -23xy + 4x2 + -4x2 + -6y2 + 6y2

Combine like terms: 23xy + -23xy = 0
3 + 13x + -23xy + 8x2 + 6y2 = 0 + 4x2 + -4x2 + -6y2 + 6y2
3 + 13x + -23xy + 8x2 + 6y2 = 4x2 + -4x2 + -6y2 + 6y2

Combine like terms: 4x2 + -4x2 = 0
3 + 13x + -23xy + 8x2 + 6y2 = 0 + -6y2 + 6y2
3 + 13x + -23xy + 8x2 + 6y2 = -6y2 + 6y2

Combine like terms: -6y2 + 6y2 = 0
3 + 13x + -23xy + 8x2 + 6y2 = 0

The solution to this equation could not be determined.

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