(4x+1)(2x-1)=(y+1)(y-3)

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Solution for (4x+1)(2x-1)=(y+1)(y-3) equation: 


Simplifying
(4x + 1)(2x + -1) = (y + 1)(y + -3)

Reorder the terms:
(1 + 4x)(2x + -1) = (y + 1)(y + -3)

Reorder the terms:
(1 + 4x)(-1 + 2x) = (y + 1)(y + -3)

Multiply (1 + 4x) * (-1 + 2x)
(1(-1 + 2x) + 4x * (-1 + 2x)) = (y + 1)(y + -3)
((-1 * 1 + 2x * 1) + 4x * (-1 + 2x)) = (y + 1)(y + -3)
((-1 + 2x) + 4x * (-1 + 2x)) = (y + 1)(y + -3)
(-1 + 2x + (-1 * 4x + 2x * 4x)) = (y + 1)(y + -3)
(-1 + 2x + (-4x + 8x2)) = (y + 1)(y + -3)

Combine like terms: 2x + -4x = -2x
(-1 + -2x + 8x2) = (y + 1)(y + -3)

Reorder the terms:
-1 + -2x + 8x2 = (1 + y)(y + -3)

Reorder the terms:
-1 + -2x + 8x2 = (1 + y)(-3 + y)

Multiply (1 + y) * (-3 + y)
-1 + -2x + 8x2 = (1(-3 + y) + y(-3 + y))
-1 + -2x + 8x2 = ((-3 * 1 + y * 1) + y(-3 + y))
-1 + -2x + 8x2 = ((-3 + 1y) + y(-3 + y))
-1 + -2x + 8x2 = (-3 + 1y + (-3 * y + y * y))
-1 + -2x + 8x2 = (-3 + 1y + (-3y + y2))

Combine like terms: 1y + -3y = -2y
-1 + -2x + 8x2 = (-3 + -2y + y2)

Solving
-1 + -2x + 8x2 = -3 + -2y + y2

Solving for variable 'x'.

Reorder the terms:
-1 + 3 + -2x + 8x2 + 2y + -1y2 = -3 + -2y + y2 + 3 + 2y + -1y2

Combine like terms: -1 + 3 = 2
2 + -2x + 8x2 + 2y + -1y2 = -3 + -2y + y2 + 3 + 2y + -1y2

Reorder the terms:
2 + -2x + 8x2 + 2y + -1y2 = -3 + 3 + -2y + 2y + y2 + -1y2

Combine like terms: -3 + 3 = 0
2 + -2x + 8x2 + 2y + -1y2 = 0 + -2y + 2y + y2 + -1y2
2 + -2x + 8x2 + 2y + -1y2 = -2y + 2y + y2 + -1y2

Combine like terms: -2y + 2y = 0
2 + -2x + 8x2 + 2y + -1y2 = 0 + y2 + -1y2
2 + -2x + 8x2 + 2y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
2 + -2x + 8x2 + 2y + -1y2 = 0

The solution to this equation could not be determined.

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