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Simplifying x3 + px2 + qx + 13 = (x2 + 4px + 6)(x + 3) + (x + -5) Reorder the terms: 13 + px2 + qx + x3 = (x2 + 4px + 6)(x + 3) + (x + -5) Reorder the terms: 13 + px2 + qx + x3 = (6 + 4px + x2)(x + 3) + (x + -5) Reorder the terms: 13 + px2 + qx + x3 = (6 + 4px + x2)(3 + x) + (x + -5) Multiply (6 + 4px + x2) * (3 + x) 13 + px2 + qx + x3 = (6(3 + x) + 4px * (3 + x) + x2(3 + x)) + (x + -5) 13 + px2 + qx + x3 = ((3 * 6 + x * 6) + 4px * (3 + x) + x2(3 + x)) + (x + -5) 13 + px2 + qx + x3 = ((18 + 6x) + 4px * (3 + x) + x2(3 + x)) + (x + -5) 13 + px2 + qx + x3 = (18 + 6x + (3 * 4px + x * 4px) + x2(3 + x)) + (x + -5) 13 + px2 + qx + x3 = (18 + 6x + (12px + 4px2) + x2(3 + x)) + (x + -5) 13 + px2 + qx + x3 = (18 + 6x + 12px + 4px2 + (3 * x2 + x * x2)) + (x + -5) 13 + px2 + qx + x3 = (18 + 6x + 12px + 4px2 + (3x2 + x3)) + (x + -5) Reorder the terms: 13 + px2 + qx + x3 = (18 + 12px + 4px2 + 6x + 3x2 + x3) + (x + -5) 13 + px2 + qx + x3 = (18 + 12px + 4px2 + 6x + 3x2 + x3) + (x + -5) Reorder the terms: 13 + px2 + qx + x3 = 18 + 12px + 4px2 + 6x + 3x2 + x3 + (-5 + x) Remove parenthesis around (-5 + x) 13 + px2 + qx + x3 = 18 + 12px + 4px2 + 6x + 3x2 + x3 + -5 + x Reorder the terms: 13 + px2 + qx + x3 = 18 + -5 + 12px + 4px2 + 6x + x + 3x2 + x3 Combine like terms: 18 + -5 = 13 13 + px2 + qx + x3 = 13 + 12px + 4px2 + 6x + x + 3x2 + x3 Combine like terms: 6x + x = 7x 13 + px2 + qx + x3 = 13 + 12px + 4px2 + 7x + 3x2 + x3 Add '-13' to each side of the equation. 13 + px2 + qx + -13 + x3 = 13 + 12px + 4px2 + 7x + 3x2 + -13 + x3 Reorder the terms: 13 + -13 + px2 + qx + x3 = 13 + 12px + 4px2 + 7x + 3x2 + -13 + x3 Combine like terms: 13 + -13 = 0 0 + px2 + qx + x3 = 13 + 12px + 4px2 + 7x + 3x2 + -13 + x3 px2 + qx + x3 = 13 + 12px + 4px2 + 7x + 3x2 + -13 + x3 Reorder the terms: px2 + qx + x3 = 13 + -13 + 12px + 4px2 + 7x + 3x2 + x3 Combine like terms: 13 + -13 = 0 px2 + qx + x3 = 0 + 12px + 4px2 + 7x + 3x2 + x3 px2 + qx + x3 = 12px + 4px2 + 7x + 3x2 + x3 Add '-1x3' to each side of the equation. px2 + qx + x3 + -1x3 = 12px + 4px2 + 7x + 3x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 px2 + qx + 0 = 12px + 4px2 + 7x + 3x2 + x3 + -1x3 px2 + qx = 12px + 4px2 + 7x + 3x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 px2 + qx = 12px + 4px2 + 7x + 3x2 + 0 px2 + qx = 12px + 4px2 + 7x + 3x2 Solving px2 + qx = 12px + 4px2 + 7x + 3x2 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12px' to each side of the equation. px2 + -12px + qx = 12px + 4px2 + 7x + -12px + 3x2 Reorder the terms: -12px + px2 + qx = 12px + 4px2 + 7x + -12px + 3x2 Reorder the terms: -12px + px2 + qx = 12px + -12px + 4px2 + 7x + 3x2 Combine like terms: 12px + -12px = 0 -12px + px2 + qx = 0 + 4px2 + 7x + 3x2 -12px + px2 + qx = 4px2 + 7x + 3x2 Add '-4px2' to each side of the equation. -12px + px2 + -4px2 + qx = 4px2 + 7x + -4px2 + 3x2 Combine like terms: px2 + -4px2 = -3px2 -12px + -3px2 + qx = 4px2 + 7x + -4px2 + 3x2 Reorder the terms: -12px + -3px2 + qx = 4px2 + -4px2 + 7x + 3x2 Combine like terms: 4px2 + -4px2 = 0 -12px + -3px2 + qx = 0 + 7x + 3x2 -12px + -3px2 + qx = 7x + 3x2 Add '-1qx' to each side of the equation. -12px + -3px2 + qx + -1qx = 7x + -1qx + 3x2 Combine like terms: qx + -1qx = 0 -12px + -3px2 + 0 = 7x + -1qx + 3x2 -12px + -3px2 = 7x + -1qx + 3x2 Reorder the terms: -12px + -3px2 = -1qx + 7x + 3x2 Reorder the terms: -12px + -3px2 + qx + -7x + -3x2 = -1qx + qx + 7x + -7x + 3x2 + -3x2 Combine like terms: -1qx + qx = 0 -12px + -3px2 + qx + -7x + -3x2 = 0 + 7x + -7x + 3x2 + -3x2 -12px + -3px2 + qx + -7x + -3x2 = 7x + -7x + 3x2 + -3x2 Combine like terms: 7x + -7x = 0 -12px + -3px2 + qx + -7x + -3x2 = 0 + 3x2 + -3x2 -12px + -3px2 + qx + -7x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -12px + -3px2 + qx + -7x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-12p + -3px + q + -7 + -3x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing p to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-12p + -3px + q + -7 + -3x)' equal to zero and attempt to solve: Simplifying -12p + -3px + q + -7 + -3x = 0 Reorder the terms: -7 + -12p + -3px + q + -3x = 0 Solving -7 + -12p + -3px + q + -3x = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + -12p + -3px + q + 7 + -3x = 0 + 7 Reorder the terms: -7 + 7 + -12p + -3px + q + -3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -12p + -3px + q + -3x = 0 + 7 -12p + -3px + q + -3x = 0 + 7 Combine like terms: 0 + 7 = 7 -12p + -3px + q + -3x = 7 Add '-1q' to each side of the equation. -12p + -3px + q + -1q + -3x = 7 + -1q Combine like terms: q + -1q = 0 -12p + -3px + 0 + -3x = 7 + -1q -12p + -3px + -3x = 7 + -1q Add '3x' to each side of the equation. -12p + -3px + -3x + 3x = 7 + -1q + 3x Combine like terms: -3x + 3x = 0 -12p + -3px + 0 = 7 + -1q + 3x -12p + -3px = 7 + -1q + 3x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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