px^2+(2p-3)y^2-4x+6y-1=0

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Solution for px^2+(2p-3)y^2-4x+6y-1=0 equation:


Simplifying
px2 + (2p + -3) * y2 + -4x + 6y + -1 = 0

Reorder the terms:
px2 + (-3 + 2p) * y2 + -4x + 6y + -1 = 0

Reorder the terms for easier multiplication:
px2 + y2(-3 + 2p) + -4x + 6y + -1 = 0
px2 + (-3 * y2 + 2p * y2) + -4x + 6y + -1 = 0

Reorder the terms:
px2 + (2py2 + -3y2) + -4x + 6y + -1 = 0
px2 + (2py2 + -3y2) + -4x + 6y + -1 = 0

Reorder the terms:
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 0

Solving
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 0

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + px2 + 2py2 + -4x + 6y + 1 + -3y2 = 0 + 1

Reorder the terms:
-1 + 1 + px2 + 2py2 + -4x + 6y + -3y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + px2 + 2py2 + -4x + 6y + -3y2 = 0 + 1
px2 + 2py2 + -4x + 6y + -3y2 = 0 + 1

Combine like terms: 0 + 1 = 1
px2 + 2py2 + -4x + 6y + -3y2 = 1

Add '4x' to each side of the equation.
px2 + 2py2 + -4x + 6y + 4x + -3y2 = 1 + 4x

Reorder the terms:
px2 + 2py2 + -4x + 4x + 6y + -3y2 = 1 + 4x

Combine like terms: -4x + 4x = 0
px2 + 2py2 + 0 + 6y + -3y2 = 1 + 4x
px2 + 2py2 + 6y + -3y2 = 1 + 4x

Add '-6y' to each side of the equation.
px2 + 2py2 + 6y + -6y + -3y2 = 1 + 4x + -6y

Combine like terms: 6y + -6y = 0
px2 + 2py2 + 0 + -3y2 = 1 + 4x + -6y
px2 + 2py2 + -3y2 = 1 + 4x + -6y

Add '3y2' to each side of the equation.
px2 + 2py2 + -3y2 + 3y2 = 1 + 4x + -6y + 3y2

Combine like terms: -3y2 + 3y2 = 0
px2 + 2py2 + 0 = 1 + 4x + -6y + 3y2
px2 + 2py2 = 1 + 4x + -6y + 3y2

Reorder the terms:
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 1 + 4x + -6y + 3y2 + -1 + -4x + 6y + -3y2

Reorder the terms:
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 1 + -1 + 4x + -4x + -6y + 6y + 3y2 + -3y2

Combine like terms: 1 + -1 = 0
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 0 + 4x + -4x + -6y + 6y + 3y2 + -3y2
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 4x + -4x + -6y + 6y + 3y2 + -3y2

Combine like terms: 4x + -4x = 0
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 0 + -6y + 6y + 3y2 + -3y2
-1 + px2 + 2py2 + -4x + 6y + -3y2 = -6y + 6y + 3y2 + -3y2

Combine like terms: -6y + 6y = 0
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 0 + 3y2 + -3y2
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-1 + px2 + 2py2 + -4x + 6y + -3y2 = 0

The solution to this equation could not be determined.

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