(5p+q)r^2-15(5p+q)r+54(5p+q)=0

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Solution for (5p+q)r^2-15(5p+q)r+54(5p+q)=0 equation: 


Simplifying
(5p + q) * r2 + -15(5p + q) * r + 54(5p + q) = 0

Reorder the terms for easier multiplication:
r2(5p + q) + -15(5p + q) * r + 54(5p + q) = 0
(5p * r2 + q * r2) + -15(5p + q) * r + 54(5p + q) = 0
(5pr2 + qr2) + -15(5p + q) * r + 54(5p + q) = 0

Reorder the terms for easier multiplication:
5pr2 + qr2 + -15r(5p + q) + 54(5p + q) = 0
5pr2 + qr2 + (5p * -15r + q * -15r) + 54(5p + q) = 0
5pr2 + qr2 + (-75pr + -15qr) + 54(5p + q) = 0
5pr2 + qr2 + -75pr + -15qr + (5p * 54 + q * 54) = 0
5pr2 + qr2 + -75pr + -15qr + (270p + 54q) = 0

Reorder the terms:
270p + -75pr + 5pr2 + 54q + -15qr + qr2 = 0

Solving
270p + -75pr + 5pr2 + 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.
270p + -75pr + 5pr2 + 54q + -15qr + -54q + qr2 = 0 + -54q

Reorder the terms:
270p + -75pr + 5pr2 + 54q + -54q + -15qr + qr2 = 0 + -54q

Combine like terms: 54q + -54q = 0
270p + -75pr + 5pr2 + 0 + -15qr + qr2 = 0 + -54q
270p + -75pr + 5pr2 + -15qr + qr2 = 0 + -54q
Remove the zero:
270p + -75pr + 5pr2 + -15qr + qr2 = -54q

Add '15qr' to each side of the equation.
270p + -75pr + 5pr2 + -15qr + 15qr + qr2 = -54q + 15qr

Combine like terms: -15qr + 15qr = 0
270p + -75pr + 5pr2 + 0 + qr2 = -54q + 15qr
270p + -75pr + 5pr2 + qr2 = -54q + 15qr

Add '-1qr2' to each side of the equation.
270p + -75pr + 5pr2 + qr2 + -1qr2 = -54q + 15qr + -1qr2

Combine like terms: qr2 + -1qr2 = 0
270p + -75pr + 5pr2 + 0 = -54q + 15qr + -1qr2
270p + -75pr + 5pr2 = -54q + 15qr + -1qr2

Reorder the terms:
270p + -75pr + 5pr2 + 54q + -15qr + qr2 = -54q + 54q + 15qr + -15qr + -1qr2 + qr2

Combine like terms: -54q + 54q = 0
270p + -75pr + 5pr2 + 54q + -15qr + qr2 = 0 + 15qr + -15qr + -1qr2 + qr2
270p + -75pr + 5pr2 + 54q + -15qr + qr2 = 15qr + -15qr + -1qr2 + qr2

Combine like terms: 15qr + -15qr = 0
270p + -75pr + 5pr2 + 54q + -15qr + qr2 = 0 + -1qr2 + qr2
270p + -75pr + 5pr2 + 54q + -15qr + qr2 = -1qr2 + qr2

Combine like terms: -1qr2 + qr2 = 0
270p + -75pr + 5pr2 + 54q + -15qr + qr2 = 0

The solution to this equation could not be determined.

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