(2p+q)r^2-15(2p+q)r+54(2p+q)=

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Solution for (2p+q)r^2-15(2p+q)r+54(2p+q)= equation: 


Simplifying
(2p + q) * r2 + -15(2p + q) * r + 54(2p + q) = 0

Reorder the terms for easier multiplication:
r2(2p + q) + -15(2p + q) * r + 54(2p + q) = 0
(2p * r2 + q * r2) + -15(2p + q) * r + 54(2p + q) = 0
(2pr2 + qr2) + -15(2p + q) * r + 54(2p + q) = 0

Reorder the terms for easier multiplication:
2pr2 + qr2 + -15r(2p + q) + 54(2p + q) = 0
2pr2 + qr2 + (2p * -15r + q * -15r) + 54(2p + q) = 0
2pr2 + qr2 + (-30pr + -15qr) + 54(2p + q) = 0
2pr2 + qr2 + -30pr + -15qr + (2p * 54 + q * 54) = 0
2pr2 + qr2 + -30pr + -15qr + (108p + 54q) = 0

Reorder the terms:
108p + -30pr + 2pr2 + 54q + -15qr + qr2 = 0

Solving
108p + -30pr + 2pr2 + 54q + -15qr + qr2 = 0

Solving for variable 'p'.

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

Add '-54q' to each side of the equation.
108p + -30pr + 2pr2 + 54q + -15qr + -54q + qr2 = 0 + -54q

Reorder the terms:
108p + -30pr + 2pr2 + 54q + -54q + -15qr + qr2 = 0 + -54q

Combine like terms: 54q + -54q = 0
108p + -30pr + 2pr2 + 0 + -15qr + qr2 = 0 + -54q
108p + -30pr + 2pr2 + -15qr + qr2 = 0 + -54q
Remove the zero:
108p + -30pr + 2pr2 + -15qr + qr2 = -54q

Add '15qr' to each side of the equation.
108p + -30pr + 2pr2 + -15qr + 15qr + qr2 = -54q + 15qr

Combine like terms: -15qr + 15qr = 0
108p + -30pr + 2pr2 + 0 + qr2 = -54q + 15qr
108p + -30pr + 2pr2 + qr2 = -54q + 15qr

Add '-1qr2' to each side of the equation.
108p + -30pr + 2pr2 + qr2 + -1qr2 = -54q + 15qr + -1qr2

Combine like terms: qr2 + -1qr2 = 0
108p + -30pr + 2pr2 + 0 = -54q + 15qr + -1qr2
108p + -30pr + 2pr2 = -54q + 15qr + -1qr2

Reorder the terms:
108p + -30pr + 2pr2 + 54q + -15qr + qr2 = -54q + 54q + 15qr + -15qr + -1qr2 + qr2

Combine like terms: -54q + 54q = 0
108p + -30pr + 2pr2 + 54q + -15qr + qr2 = 0 + 15qr + -15qr + -1qr2 + qr2
108p + -30pr + 2pr2 + 54q + -15qr + qr2 = 15qr + -15qr + -1qr2 + qr2

Combine like terms: 15qr + -15qr = 0
108p + -30pr + 2pr2 + 54q + -15qr + qr2 = 0 + -1qr2 + qr2
108p + -30pr + 2pr2 + 54q + -15qr + qr2 = -1qr2 + qr2

Combine like terms: -1qr2 + qr2 = 0
108p + -30pr + 2pr2 + 54q + -15qr + qr2 = 0

The solution to this equation could not be determined.

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