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Simplifying (x + -4)(px2 + qx + r) = 0 Reorder the terms: (-4 + x)(px2 + qx + r) = 0 Multiply (-4 + x) * (px2 + qx + r) (-4(px2 + qx + r) + x(px2 + qx + r)) = 0 ((px2 * -4 + qx * -4 + r * -4) + x(px2 + qx + r)) = 0 ((-4px2 + -4qx + -4r) + x(px2 + qx + r)) = 0 (-4px2 + -4qx + -4r + (px2 * x + qx * x + r * x)) = 0 (-4px2 + -4qx + -4r + (px3 + qx2 + rx)) = 0 Reorder the terms: (-4px2 + px3 + -4qx + qx2 + -4r + rx) = 0 (-4px2 + px3 + -4qx + qx2 + -4r + rx) = 0 Solving -4px2 + px3 + -4qx + qx2 + -4r + rx = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4qx' to each side of the equation. -4px2 + px3 + -4qx + qx2 + -4r + 4qx + rx = 0 + 4qx Reorder the terms: -4px2 + px3 + -4qx + 4qx + qx2 + -4r + rx = 0 + 4qx Combine like terms: -4qx + 4qx = 0 -4px2 + px3 + 0 + qx2 + -4r + rx = 0 + 4qx -4px2 + px3 + qx2 + -4r + rx = 0 + 4qx Remove the zero: -4px2 + px3 + qx2 + -4r + rx = 4qx Add '-1qx2' to each side of the equation. -4px2 + px3 + qx2 + -4r + -1qx2 + rx = 4qx + -1qx2 Reorder the terms: -4px2 + px3 + qx2 + -1qx2 + -4r + rx = 4qx + -1qx2 Combine like terms: qx2 + -1qx2 = 0 -4px2 + px3 + 0 + -4r + rx = 4qx + -1qx2 -4px2 + px3 + -4r + rx = 4qx + -1qx2 Add '4r' to each side of the equation. -4px2 + px3 + -4r + 4r + rx = 4qx + -1qx2 + 4r Combine like terms: -4r + 4r = 0 -4px2 + px3 + 0 + rx = 4qx + -1qx2 + 4r -4px2 + px3 + rx = 4qx + -1qx2 + 4r Add '-1rx' to each side of the equation. -4px2 + px3 + rx + -1rx = 4qx + -1qx2 + 4r + -1rx Combine like terms: rx + -1rx = 0 -4px2 + px3 + 0 = 4qx + -1qx2 + 4r + -1rx -4px2 + px3 = 4qx + -1qx2 + 4r + -1rx Reorder the terms: -4px2 + px3 + -4qx + qx2 + -4r + rx = 4qx + -4qx + -1qx2 + qx2 + 4r + -4r + -1rx + rx Combine like terms: 4qx + -4qx = 0 -4px2 + px3 + -4qx + qx2 + -4r + rx = 0 + -1qx2 + qx2 + 4r + -4r + -1rx + rx -4px2 + px3 + -4qx + qx2 + -4r + rx = -1qx2 + qx2 + 4r + -4r + -1rx + rx Combine like terms: -1qx2 + qx2 = 0 -4px2 + px3 + -4qx + qx2 + -4r + rx = 0 + 4r + -4r + -1rx + rx -4px2 + px3 + -4qx + qx2 + -4r + rx = 4r + -4r + -1rx + rx Combine like terms: 4r + -4r = 0 -4px2 + px3 + -4qx + qx2 + -4r + rx = 0 + -1rx + rx -4px2 + px3 + -4qx + qx2 + -4r + rx = -1rx + rx Combine like terms: -1rx + rx = 0 -4px2 + px3 + -4qx + qx2 + -4r + rx = 0 The solution to this equation could not be determined.
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