(2x+3y)(px+qy)=(r*x*x)+23y+(12*y*y)

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


Simplifying
(2x + 3y)(px + qy) = (r * x * x) + 23y + (12y * y)

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

Reorder the terms:
(3pxy + 2px2 + 2qxy + 3qy2) = (r * x * x) + 23y + (12y * y)
(3pxy + 2px2 + 2qxy + 3qy2) = (r * x * x) + 23y + (12y * y)

Multiply r * x
3pxy + 2px2 + 2qxy + 3qy2 = (rx * x) + 23y + (12y * y)

Multiply rx * x
3pxy + 2px2 + 2qxy + 3qy2 = (rx2) + 23y + (12y * y)
3pxy + 2px2 + 2qxy + 3qy2 = rx2 + 23y + (12y * y)

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

Solving
3pxy + 2px2 + 2qxy + 3qy2 = rx2 + 23y + (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 + 23y + -2qxy + (12y2)

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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