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Simplifying (5p + q) * r2 + -11(5p + q) * r + 24(5p + q) = 0 Reorder the terms for easier multiplication: r2(5p + q) + -11(5p + q) * r + 24(5p + q) = 0 (5p * r2 + q * r2) + -11(5p + q) * r + 24(5p + q) = 0 (5pr2 + qr2) + -11(5p + q) * r + 24(5p + q) = 0 Reorder the terms for easier multiplication: 5pr2 + qr2 + -11r(5p + q) + 24(5p + q) = 0 5pr2 + qr2 + (5p * -11r + q * -11r) + 24(5p + q) = 0 5pr2 + qr2 + (-55pr + -11qr) + 24(5p + q) = 0 5pr2 + qr2 + -55pr + -11qr + (5p * 24 + q * 24) = 0 5pr2 + qr2 + -55pr + -11qr + (120p + 24q) = 0 Reorder the terms: 120p + -55pr + 5pr2 + 24q + -11qr + qr2 = 0 Solving 120p + -55pr + 5pr2 + 24q + -11qr + qr2 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-24q' to each side of the equation. 120p + -55pr + 5pr2 + 24q + -11qr + -24q + qr2 = 0 + -24q Reorder the terms: 120p + -55pr + 5pr2 + 24q + -24q + -11qr + qr2 = 0 + -24q Combine like terms: 24q + -24q = 0 120p + -55pr + 5pr2 + 0 + -11qr + qr2 = 0 + -24q 120p + -55pr + 5pr2 + -11qr + qr2 = 0 + -24q Remove the zero: 120p + -55pr + 5pr2 + -11qr + qr2 = -24q Add '11qr' to each side of the equation. 120p + -55pr + 5pr2 + -11qr + 11qr + qr2 = -24q + 11qr Combine like terms: -11qr + 11qr = 0 120p + -55pr + 5pr2 + 0 + qr2 = -24q + 11qr 120p + -55pr + 5pr2 + qr2 = -24q + 11qr Add '-1qr2' to each side of the equation. 120p + -55pr + 5pr2 + qr2 + -1qr2 = -24q + 11qr + -1qr2 Combine like terms: qr2 + -1qr2 = 0 120p + -55pr + 5pr2 + 0 = -24q + 11qr + -1qr2 120p + -55pr + 5pr2 = -24q + 11qr + -1qr2 Reorder the terms: 120p + -55pr + 5pr2 + 24q + -11qr + qr2 = -24q + 24q + 11qr + -11qr + -1qr2 + qr2 Combine like terms: -24q + 24q = 0 120p + -55pr + 5pr2 + 24q + -11qr + qr2 = 0 + 11qr + -11qr + -1qr2 + qr2 120p + -55pr + 5pr2 + 24q + -11qr + qr2 = 11qr + -11qr + -1qr2 + qr2 Combine like terms: 11qr + -11qr = 0 120p + -55pr + 5pr2 + 24q + -11qr + qr2 = 0 + -1qr2 + qr2 120p + -55pr + 5pr2 + 24q + -11qr + qr2 = -1qr2 + qr2 Combine like terms: -1qr2 + qr2 = 0 120p + -55pr + 5pr2 + 24q + -11qr + qr2 = 0 The solution to this equation could not be determined.
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