(2x+3y)*(px+qy)=rx^2+23xy+12y^2

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Solution for (2x+3y)*(px+qy)=rx^2+23xy+12y^2 equation: 


Simplifying
(2x + 3y)(px + qy) = rx2 + 23xy + 12y2

Multiply (2x + 3y) * (px + qy)
(2x * (px + qy) + 3y * (px + qy)) = rx2 + 23xy + 12y2
((px * 2x + qy * 2x) + 3y * (px + qy)) = rx2 + 23xy + 12y2
((2px2 + 2qxy) + 3y * (px + qy)) = rx2 + 23xy + 12y2
(2px2 + 2qxy + (px * 3y + qy * 3y)) = rx2 + 23xy + 12y2
(2px2 + 2qxy + (3pxy + 3qy2)) = rx2 + 23xy + 12y2

Reorder the terms:
(3pxy + 2px2 + 2qxy + 3qy2) = rx2 + 23xy + 12y2
(3pxy + 2px2 + 2qxy + 3qy2) = rx2 + 23xy + 12y2

Solving
3pxy + 2px2 + 2qxy + 3qy2 = rx2 + 23xy + 12y2

Solving for variable 'p'.

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

Add '-2qxy' to each side of the equation.
3pxy + 2px2 + 2qxy + -2qxy + 3qy2 = rx2 + 23xy + -2qxy + 12y2

Combine like terms: 2qxy + -2qxy = 0
3pxy + 2px2 + 0 + 3qy2 = rx2 + 23xy + -2qxy + 12y2
3pxy + 2px2 + 3qy2 = rx2 + 23xy + -2qxy + 12y2

Reorder the terms:
3pxy + 2px2 + 3qy2 = -2qxy + rx2 + 23xy + 12y2

Add '-3qy2' to each side of the equation.
3pxy + 2px2 + 3qy2 + -3qy2 = -2qxy + rx2 + 23xy + -3qy2 + 12y2

Combine like terms: 3qy2 + -3qy2 = 0
3pxy + 2px2 + 0 = -2qxy + rx2 + 23xy + -3qy2 + 12y2
3pxy + 2px2 = -2qxy + rx2 + 23xy + -3qy2 + 12y2

Reorder the terms:
3pxy + 2px2 = -2qxy + -3qy2 + rx2 + 23xy + 12y2

Reorder the terms:
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = -2qxy + 2qxy + -3qy2 + 3qy2 + rx2 + -1rx2 + 23xy + -23xy + 12y2 + -12y2

Combine like terms: -2qxy + 2qxy = 0
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = 0 + -3qy2 + 3qy2 + rx2 + -1rx2 + 23xy + -23xy + 12y2 + -12y2
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = -3qy2 + 3qy2 + rx2 + -1rx2 + 23xy + -23xy + 12y2 + -12y2

Combine like terms: -3qy2 + 3qy2 = 0
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = 0 + rx2 + -1rx2 + 23xy + -23xy + 12y2 + -12y2
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = rx2 + -1rx2 + 23xy + -23xy + 12y2 + -12y2

Combine like terms: rx2 + -1rx2 = 0
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = 0 + 23xy + -23xy + 12y2 + -12y2
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = 23xy + -23xy + 12y2 + -12y2

Combine like terms: 23xy + -23xy = 0
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = 0 + 12y2 + -12y2
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = 12y2 + -12y2

Combine like terms: 12y2 + -12y2 = 0
3pxy + 2px2 + 2qxy + 3qy2 + -1rx2 + -23xy + -12y2 = 0

The solution to this equation could not be determined.

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