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Simplifying (x + -1p)(2x2 + 9x + 10) = (x2 + -4)(2x + q) Reorder the terms: (-1p + x)(2x2 + 9x + 10) = (x2 + -4)(2x + q) Reorder the terms: (-1p + x)(10 + 9x + 2x2) = (x2 + -4)(2x + q) Multiply (-1p + x) * (10 + 9x + 2x2) (-1p * (10 + 9x + 2x2) + x(10 + 9x + 2x2)) = (x2 + -4)(2x + q) ((10 * -1p + 9x * -1p + 2x2 * -1p) + x(10 + 9x + 2x2)) = (x2 + -4)(2x + q) ((-10p + -9px + -2px2) + x(10 + 9x + 2x2)) = (x2 + -4)(2x + q) (-10p + -9px + -2px2 + (10 * x + 9x * x + 2x2 * x)) = (x2 + -4)(2x + q) (-10p + -9px + -2px2 + (10x + 9x2 + 2x3)) = (x2 + -4)(2x + q) (-10p + -9px + -2px2 + 10x + 9x2 + 2x3) = (x2 + -4)(2x + q) Reorder the terms: -10p + -9px + -2px2 + 10x + 9x2 + 2x3 = (-4 + x2)(2x + q) Reorder the terms: -10p + -9px + -2px2 + 10x + 9x2 + 2x3 = (-4 + x2)(q + 2x) Multiply (-4 + x2) * (q + 2x) -10p + -9px + -2px2 + 10x + 9x2 + 2x3 = (-4(q + 2x) + x2(q + 2x)) -10p + -9px + -2px2 + 10x + 9x2 + 2x3 = ((q * -4 + 2x * -4) + x2(q + 2x)) -10p + -9px + -2px2 + 10x + 9x2 + 2x3 = ((-4q + -8x) + x2(q + 2x)) -10p + -9px + -2px2 + 10x + 9x2 + 2x3 = (-4q + -8x + (q * x2 + 2x * x2)) -10p + -9px + -2px2 + 10x + 9x2 + 2x3 = (-4q + -8x + (qx2 + 2x3)) Reorder the terms: -10p + -9px + -2px2 + 10x + 9x2 + 2x3 = (-4q + qx2 + -8x + 2x3) -10p + -9px + -2px2 + 10x + 9x2 + 2x3 = (-4q + qx2 + -8x + 2x3) Add '-2x3' to each side of the equation. -10p + -9px + -2px2 + 10x + 9x2 + 2x3 + -2x3 = -4q + qx2 + -8x + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -10p + -9px + -2px2 + 10x + 9x2 + 0 = -4q + qx2 + -8x + 2x3 + -2x3 -10p + -9px + -2px2 + 10x + 9x2 = -4q + qx2 + -8x + 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -10p + -9px + -2px2 + 10x + 9x2 = -4q + qx2 + -8x + 0 -10p + -9px + -2px2 + 10x + 9x2 = -4q + qx2 + -8x Solving -10p + -9px + -2px2 + 10x + 9x2 = -4q + qx2 + -8x Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10x' to each side of the equation. -10p + -9px + -2px2 + 10x + -10x + 9x2 = -4q + qx2 + -8x + -10x Combine like terms: 10x + -10x = 0 -10p + -9px + -2px2 + 0 + 9x2 = -4q + qx2 + -8x + -10x -10p + -9px + -2px2 + 9x2 = -4q + qx2 + -8x + -10x Combine like terms: -8x + -10x = -18x -10p + -9px + -2px2 + 9x2 = -4q + qx2 + -18x Add '-9x2' to each side of the equation. -10p + -9px + -2px2 + 9x2 + -9x2 = -4q + qx2 + -18x + -9x2 Combine like terms: 9x2 + -9x2 = 0 -10p + -9px + -2px2 + 0 = -4q + qx2 + -18x + -9x2 -10p + -9px + -2px2 = -4q + qx2 + -18x + -9x2 Reorder the terms: -10p + -9px + -2px2 + 4q + -1qx2 + 18x + 9x2 = -4q + 4q + qx2 + -1qx2 + -18x + 18x + -9x2 + 9x2 Combine like terms: -4q + 4q = 0 -10p + -9px + -2px2 + 4q + -1qx2 + 18x + 9x2 = 0 + qx2 + -1qx2 + -18x + 18x + -9x2 + 9x2 -10p + -9px + -2px2 + 4q + -1qx2 + 18x + 9x2 = qx2 + -1qx2 + -18x + 18x + -9x2 + 9x2 Combine like terms: qx2 + -1qx2 = 0 -10p + -9px + -2px2 + 4q + -1qx2 + 18x + 9x2 = 0 + -18x + 18x + -9x2 + 9x2 -10p + -9px + -2px2 + 4q + -1qx2 + 18x + 9x2 = -18x + 18x + -9x2 + 9x2 Combine like terms: -18x + 18x = 0 -10p + -9px + -2px2 + 4q + -1qx2 + 18x + 9x2 = 0 + -9x2 + 9x2 -10p + -9px + -2px2 + 4q + -1qx2 + 18x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -10p + -9px + -2px2 + 4q + -1qx2 + 18x + 9x2 = 0 The solution to this equation could not be determined.
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