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Simplifying (X + 1)(x + -6)(7 + -14x) = 0 Reorder the terms: (1 + X)(x + -6)(7 + -14x) = 0 Reorder the terms: (1 + X)(-6 + x)(7 + -14x) = 0 Multiply (1 + X) * (-6 + x) (1(-6 + x) + X(-6 + x))(7 + -14x) = 0 ((-6 * 1 + x * 1) + X(-6 + x))(7 + -14x) = 0 ((-6 + 1x) + X(-6 + x))(7 + -14x) = 0 (-6 + 1x + (-6 * X + x * X))(7 + -14x) = 0 (-6 + 1x + (-6X + xX))(7 + -14x) = 0 Reorder the terms: (-6 + -6X + 1x + xX)(7 + -14x) = 0 (-6 + -6X + 1x + xX)(7 + -14x) = 0 Multiply (-6 + -6X + 1x + xX) * (7 + -14x) (-6(7 + -14x) + -6X * (7 + -14x) + 1x * (7 + -14x) + xX(7 + -14x)) = 0 ((7 * -6 + -14x * -6) + -6X * (7 + -14x) + 1x * (7 + -14x) + xX(7 + -14x)) = 0 ((-42 + 84x) + -6X * (7 + -14x) + 1x * (7 + -14x) + xX(7 + -14x)) = 0 (-42 + 84x + (7 * -6X + -14x * -6X) + 1x * (7 + -14x) + xX(7 + -14x)) = 0 (-42 + 84x + (-42X + 84xX) + 1x * (7 + -14x) + xX(7 + -14x)) = 0 (-42 + 84x + -42X + 84xX + (7 * 1x + -14x * 1x) + xX(7 + -14x)) = 0 (-42 + 84x + -42X + 84xX + (7x + -14x2) + xX(7 + -14x)) = 0 (-42 + 84x + -42X + 84xX + 7x + -14x2 + (7 * xX + -14x * xX)) = 0 (-42 + 84x + -42X + 84xX + 7x + -14x2 + (7xX + -14x2X)) = 0 Reorder the terms: (-42 + -42X + 84x + 7x + 84xX + 7xX + -14x2 + -14x2X) = 0 Combine like terms: 84x + 7x = 91x (-42 + -42X + 91x + 84xX + 7xX + -14x2 + -14x2X) = 0 Combine like terms: 84xX + 7xX = 91xX (-42 + -42X + 91x + 91xX + -14x2 + -14x2X) = 0 Solving -42 + -42X + 91x + 91xX + -14x2 + -14x2X = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '42' to each side of the equation. -42 + -42X + 91x + 91xX + -14x2 + 42 + -14x2X = 0 + 42 Reorder the terms: -42 + 42 + -42X + 91x + 91xX + -14x2 + -14x2X = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -42X + 91x + 91xX + -14x2 + -14x2X = 0 + 42 -42X + 91x + 91xX + -14x2 + -14x2X = 0 + 42 Combine like terms: 0 + 42 = 42 -42X + 91x + 91xX + -14x2 + -14x2X = 42 Add '-91x' to each side of the equation. -42X + 91x + 91xX + -14x2 + -91x + -14x2X = 42 + -91x Reorder the terms: -42X + 91x + -91x + 91xX + -14x2 + -14x2X = 42 + -91x Combine like terms: 91x + -91x = 0 -42X + 0 + 91xX + -14x2 + -14x2X = 42 + -91x -42X + 91xX + -14x2 + -14x2X = 42 + -91x Add '14x2' to each side of the equation. -42X + 91xX + -14x2 + 14x2 + -14x2X = 42 + -91x + 14x2 Combine like terms: -14x2 + 14x2 = 0 -42X + 91xX + 0 + -14x2X = 42 + -91x + 14x2 -42X + 91xX + -14x2X = 42 + -91x + 14x2 Reorder the terms: -42 + -42X + 91x + 91xX + -14x2 + -14x2X = 42 + -91x + 14x2 + -42 + 91x + -14x2 Reorder the terms: -42 + -42X + 91x + 91xX + -14x2 + -14x2X = 42 + -42 + -91x + 91x + 14x2 + -14x2 Combine like terms: 42 + -42 = 0 -42 + -42X + 91x + 91xX + -14x2 + -14x2X = 0 + -91x + 91x + 14x2 + -14x2 -42 + -42X + 91x + 91xX + -14x2 + -14x2X = -91x + 91x + 14x2 + -14x2 Combine like terms: -91x + 91x = 0 -42 + -42X + 91x + 91xX + -14x2 + -14x2X = 0 + 14x2 + -14x2 -42 + -42X + 91x + 91xX + -14x2 + -14x2X = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -42 + -42X + 91x + 91xX + -14x2 + -14x2X = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-6 + -6X + 13x + 13xX + -2x2 + -2x2X) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-6 + -6X + 13x + 13xX + -2x2 + -2x2X)' equal to zero and attempt to solve: Simplifying -6 + -6X + 13x + 13xX + -2x2 + -2x2X = 0 Solving -6 + -6X + 13x + 13xX + -2x2 + -2x2X = 0 Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + -6X + 13x + 13xX + -2x2 + 6 + -2x2X = 0 + 6 Reorder the terms: -6 + 6 + -6X + 13x + 13xX + -2x2 + -2x2X = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6X + 13x + 13xX + -2x2 + -2x2X = 0 + 6 -6X + 13x + 13xX + -2x2 + -2x2X = 0 + 6 Combine like terms: 0 + 6 = 6 -6X + 13x + 13xX + -2x2 + -2x2X = 6 Add '-13x' to each side of the equation. -6X + 13x + 13xX + -2x2 + -13x + -2x2X = 6 + -13x Reorder the terms: -6X + 13x + -13x + 13xX + -2x2 + -2x2X = 6 + -13x Combine like terms: 13x + -13x = 0 -6X + 0 + 13xX + -2x2 + -2x2X = 6 + -13x -6X + 13xX + -2x2 + -2x2X = 6 + -13x Add '2x2' to each side of the equation. -6X + 13xX + -2x2 + 2x2 + -2x2X = 6 + -13x + 2x2 Combine like terms: -2x2 + 2x2 = 0 -6X + 13xX + 0 + -2x2X = 6 + -13x + 2x2 -6X + 13xX + -2x2X = 6 + -13x + 2x2 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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