(px+2)(3x+q)=rx^2+x-2

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Solution for (px+2)(3x+q)=rx^2+x-2 equation: 


Simplifying
(px + 2)(3x + q) = rx2 + x + -2

Reorder the terms:
(2 + px)(3x + q) = rx2 + x + -2

Reorder the terms:
(2 + px)(q + 3x) = rx2 + x + -2

Multiply (2 + px) * (q + 3x)
(2(q + 3x) + px(q + 3x)) = rx2 + x + -2
((q * 2 + 3x * 2) + px(q + 3x)) = rx2 + x + -2
((2q + 6x) + px(q + 3x)) = rx2 + x + -2
(2q + 6x + (q * px + 3x * px)) = rx2 + x + -2
(2q + 6x + (pqx + 3px2)) = rx2 + x + -2

Reorder the terms:
(pqx + 3px2 + 2q + 6x) = rx2 + x + -2
(pqx + 3px2 + 2q + 6x) = rx2 + x + -2

Reorder the terms:
pqx + 3px2 + 2q + 6x = -2 + rx2 + x

Solving
pqx + 3px2 + 2q + 6x = -2 + rx2 + x

Solving for variable 'p'.

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

Add '-2q' to each side of the equation.
pqx + 3px2 + 2q + -2q + 6x = -2 + rx2 + -2q + x

Combine like terms: 2q + -2q = 0
pqx + 3px2 + 0 + 6x = -2 + rx2 + -2q + x
pqx + 3px2 + 6x = -2 + rx2 + -2q + x

Reorder the terms:
pqx + 3px2 + 6x = -2 + -2q + rx2 + x

Add '-6x' to each side of the equation.
pqx + 3px2 + 6x + -6x = -2 + -2q + rx2 + x + -6x

Combine like terms: 6x + -6x = 0
pqx + 3px2 + 0 = -2 + -2q + rx2 + x + -6x
pqx + 3px2 = -2 + -2q + rx2 + x + -6x

Combine like terms: x + -6x = -5x
pqx + 3px2 = -2 + -2q + rx2 + -5x

Reorder the terms:
2 + pqx + 3px2 + 2q + -1rx2 + 5x = -2 + -2q + rx2 + -5x + 2 + 2q + -1rx2 + 5x

Reorder the terms:
2 + pqx + 3px2 + 2q + -1rx2 + 5x = -2 + 2 + -2q + 2q + rx2 + -1rx2 + -5x + 5x

Combine like terms: -2 + 2 = 0
2 + pqx + 3px2 + 2q + -1rx2 + 5x = 0 + -2q + 2q + rx2 + -1rx2 + -5x + 5x
2 + pqx + 3px2 + 2q + -1rx2 + 5x = -2q + 2q + rx2 + -1rx2 + -5x + 5x

Combine like terms: -2q + 2q = 0
2 + pqx + 3px2 + 2q + -1rx2 + 5x = 0 + rx2 + -1rx2 + -5x + 5x
2 + pqx + 3px2 + 2q + -1rx2 + 5x = rx2 + -1rx2 + -5x + 5x

Combine like terms: rx2 + -1rx2 = 0
2 + pqx + 3px2 + 2q + -1rx2 + 5x = 0 + -5x + 5x
2 + pqx + 3px2 + 2q + -1rx2 + 5x = -5x + 5x

Combine like terms: -5x + 5x = 0
2 + pqx + 3px2 + 2q + -1rx2 + 5x = 0

The solution to this equation could not be determined.

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