(2p+q)r^2-12(2p+q)r+27(2p+q)=

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Solution for (2p+q)r^2-12(2p+q)r+27(2p+q)= equation: 


Simplifying
(2p + q) * r2 + -12(2p + q) * r + 27(2p + q) = 0

Reorder the terms for easier multiplication:
r2(2p + q) + -12(2p + q) * r + 27(2p + q) = 0
(2p * r2 + q * r2) + -12(2p + q) * r + 27(2p + q) = 0
(2pr2 + qr2) + -12(2p + q) * r + 27(2p + q) = 0

Reorder the terms for easier multiplication:
2pr2 + qr2 + -12r(2p + q) + 27(2p + q) = 0
2pr2 + qr2 + (2p * -12r + q * -12r) + 27(2p + q) = 0
2pr2 + qr2 + (-24pr + -12qr) + 27(2p + q) = 0
2pr2 + qr2 + -24pr + -12qr + (2p * 27 + q * 27) = 0
2pr2 + qr2 + -24pr + -12qr + (54p + 27q) = 0

Reorder the terms:
54p + -24pr + 2pr2 + 27q + -12qr + qr2 = 0

Solving
54p + -24pr + 2pr2 + 27q + -12qr + qr2 = 0

Solving for variable 'p'.

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

Add '-27q' to each side of the equation.
54p + -24pr + 2pr2 + 27q + -12qr + -27q + qr2 = 0 + -27q

Reorder the terms:
54p + -24pr + 2pr2 + 27q + -27q + -12qr + qr2 = 0 + -27q

Combine like terms: 27q + -27q = 0
54p + -24pr + 2pr2 + 0 + -12qr + qr2 = 0 + -27q
54p + -24pr + 2pr2 + -12qr + qr2 = 0 + -27q
Remove the zero:
54p + -24pr + 2pr2 + -12qr + qr2 = -27q

Add '12qr' to each side of the equation.
54p + -24pr + 2pr2 + -12qr + 12qr + qr2 = -27q + 12qr

Combine like terms: -12qr + 12qr = 0
54p + -24pr + 2pr2 + 0 + qr2 = -27q + 12qr
54p + -24pr + 2pr2 + qr2 = -27q + 12qr

Add '-1qr2' to each side of the equation.
54p + -24pr + 2pr2 + qr2 + -1qr2 = -27q + 12qr + -1qr2

Combine like terms: qr2 + -1qr2 = 0
54p + -24pr + 2pr2 + 0 = -27q + 12qr + -1qr2
54p + -24pr + 2pr2 = -27q + 12qr + -1qr2

Reorder the terms:
54p + -24pr + 2pr2 + 27q + -12qr + qr2 = -27q + 27q + 12qr + -12qr + -1qr2 + qr2

Combine like terms: -27q + 27q = 0
54p + -24pr + 2pr2 + 27q + -12qr + qr2 = 0 + 12qr + -12qr + -1qr2 + qr2
54p + -24pr + 2pr2 + 27q + -12qr + qr2 = 12qr + -12qr + -1qr2 + qr2

Combine like terms: 12qr + -12qr = 0
54p + -24pr + 2pr2 + 27q + -12qr + qr2 = 0 + -1qr2 + qr2
54p + -24pr + 2pr2 + 27q + -12qr + qr2 = -1qr2 + qr2

Combine like terms: -1qr2 + qr2 = 0
54p + -24pr + 2pr2 + 27q + -12qr + qr2 = 0

The solution to this equation could not be determined.

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