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Simplifying (5x + -3)(x + -2)(x + 1) * X = 0 Reorder the terms: (-3 + 5x)(x + -2)(x + 1) * X = 0 Reorder the terms: (-3 + 5x)(-2 + x)(x + 1) * X = 0 Reorder the terms: (-3 + 5x)(-2 + x)(1 + x) * X = 0 Reorder the terms for easier multiplication: X(-3 + 5x)(-2 + x)(1 + x) = 0 Multiply (-3 + 5x) * (-2 + x) X(-3(-2 + x) + 5x * (-2 + x))(1 + x) = 0 X((-2 * -3 + x * -3) + 5x * (-2 + x))(1 + x) = 0 X((6 + -3x) + 5x * (-2 + x))(1 + x) = 0 X(6 + -3x + (-2 * 5x + x * 5x))(1 + x) = 0 X(6 + -3x + (-10x + 5x2))(1 + x) = 0 Combine like terms: -3x + -10x = -13x X(6 + -13x + 5x2)(1 + x) = 0 Multiply (6 + -13x + 5x2) * (1 + x) X(6(1 + x) + -13x * (1 + x) + 5x2 * (1 + x)) = 0 X((1 * 6 + x * 6) + -13x * (1 + x) + 5x2 * (1 + x)) = 0 X((6 + 6x) + -13x * (1 + x) + 5x2 * (1 + x)) = 0 X(6 + 6x + (1 * -13x + x * -13x) + 5x2 * (1 + x)) = 0 X(6 + 6x + (-13x + -13x2) + 5x2 * (1 + x)) = 0 X(6 + 6x + -13x + -13x2 + (1 * 5x2 + x * 5x2)) = 0 X(6 + 6x + -13x + -13x2 + (5x2 + 5x3)) = 0 Combine like terms: 6x + -13x = -7x X(6 + -7x + -13x2 + 5x2 + 5x3) = 0 Combine like terms: -13x2 + 5x2 = -8x2 X(6 + -7x + -8x2 + 5x3) = 0 (6 * X + -7x * X + -8x2 * X + 5x3 * X) = 0 (6X + -7xX + -8x2X + 5x3X) = 0 Solving 6X + -7xX + -8x2X + 5x3X = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'X'. X(6 + -7x + -8x2 + 5x3) = 0Subproblem 1
Set the factor 'X' equal to zero and attempt to solve: Simplifying X = 0 Solving X = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X = 0Subproblem 2
Set the factor '(6 + -7x + -8x2 + 5x3)' equal to zero and attempt to solve: Simplifying 6 + -7x + -8x2 + 5x3 = 0 Solving 6 + -7x + -8x2 + 5x3 = 0 Move all terms containing X to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -7x + -8x2 + -6 + 5x3 = 0 + -6 Reorder the terms: 6 + -6 + -7x + -8x2 + 5x3 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7x + -8x2 + 5x3 = 0 + -6 -7x + -8x2 + 5x3 = 0 + -6 Combine like terms: 0 + -6 = -6 -7x + -8x2 + 5x3 = -6 Add '7x' to each side of the equation. -7x + -8x2 + 7x + 5x3 = -6 + 7x Reorder the terms: -7x + 7x + -8x2 + 5x3 = -6 + 7x Combine like terms: -7x + 7x = 0 0 + -8x2 + 5x3 = -6 + 7x -8x2 + 5x3 = -6 + 7x Add '8x2' to each side of the equation. -8x2 + 8x2 + 5x3 = -6 + 7x + 8x2 Combine like terms: -8x2 + 8x2 = 0 0 + 5x3 = -6 + 7x + 8x2 5x3 = -6 + 7x + 8x2 Add '-5x3' to each side of the equation. 5x3 + -5x3 = -6 + 7x + 8x2 + -5x3 Combine like terms: 5x3 + -5x3 = 0 0 = -6 + 7x + 8x2 + -5x3 Simplifying 0 = -6 + 7x + 8x2 + -5x3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
X = {0}
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