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Simplifying (px + q)(2x + 5) = 6x2 + 11x + r Reorder the terms: (px + q)(5 + 2x) = 6x2 + 11x + r Multiply (px + q) * (5 + 2x) (px(5 + 2x) + q(5 + 2x)) = 6x2 + 11x + r ((5 * px + 2x * px) + q(5 + 2x)) = 6x2 + 11x + r ((5px + 2px2) + q(5 + 2x)) = 6x2 + 11x + r (5px + 2px2 + (5 * q + 2x * q)) = 6x2 + 11x + r (5px + 2px2 + (5q + 2qx)) = 6x2 + 11x + r (5px + 2px2 + 5q + 2qx) = 6x2 + 11x + r Reorder the terms: 5px + 2px2 + 5q + 2qx = r + 11x + 6x2 Solving 5px + 2px2 + 5q + 2qx = r + 11x + 6x2 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5q' to each side of the equation. 5px + 2px2 + 5q + -5q + 2qx = r + 11x + -5q + 6x2 Combine like terms: 5q + -5q = 0 5px + 2px2 + 0 + 2qx = r + 11x + -5q + 6x2 5px + 2px2 + 2qx = r + 11x + -5q + 6x2 Reorder the terms: 5px + 2px2 + 2qx = -5q + r + 11x + 6x2 Add '-2qx' to each side of the equation. 5px + 2px2 + 2qx + -2qx = -5q + r + 11x + -2qx + 6x2 Combine like terms: 2qx + -2qx = 0 5px + 2px2 + 0 = -5q + r + 11x + -2qx + 6x2 5px + 2px2 = -5q + r + 11x + -2qx + 6x2 Reorder the terms: 5px + 2px2 = -5q + -2qx + r + 11x + 6x2 Reorder the terms: 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = -5q + 5q + -2qx + 2qx + r + -1r + 11x + -11x + 6x2 + -6x2 Combine like terms: -5q + 5q = 0 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = 0 + -2qx + 2qx + r + -1r + 11x + -11x + 6x2 + -6x2 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = -2qx + 2qx + r + -1r + 11x + -11x + 6x2 + -6x2 Combine like terms: -2qx + 2qx = 0 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = 0 + r + -1r + 11x + -11x + 6x2 + -6x2 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = r + -1r + 11x + -11x + 6x2 + -6x2 Combine like terms: r + -1r = 0 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = 0 + 11x + -11x + 6x2 + -6x2 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = 11x + -11x + 6x2 + -6x2 Combine like terms: 11x + -11x = 0 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = 0 + 6x2 + -6x2 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 5px + 2px2 + 5q + 2qx + -1r + -11x + -6x2 = 0 The solution to this equation could not be determined.
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