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Simplifying X(4x + -5)(x + 3)(2x + 7) = 0 Reorder the terms: X(-5 + 4x)(x + 3)(2x + 7) = 0 Reorder the terms: X(-5 + 4x)(3 + x)(2x + 7) = 0 Reorder the terms: X(-5 + 4x)(3 + x)(7 + 2x) = 0 Multiply (-5 + 4x) * (3 + x) X(-5(3 + x) + 4x * (3 + x))(7 + 2x) = 0 X((3 * -5 + x * -5) + 4x * (3 + x))(7 + 2x) = 0 X((-15 + -5x) + 4x * (3 + x))(7 + 2x) = 0 X(-15 + -5x + (3 * 4x + x * 4x))(7 + 2x) = 0 X(-15 + -5x + (12x + 4x2))(7 + 2x) = 0 Combine like terms: -5x + 12x = 7x X(-15 + 7x + 4x2)(7 + 2x) = 0 Multiply (-15 + 7x + 4x2) * (7 + 2x) X(-15(7 + 2x) + 7x * (7 + 2x) + 4x2 * (7 + 2x)) = 0 X((7 * -15 + 2x * -15) + 7x * (7 + 2x) + 4x2 * (7 + 2x)) = 0 X((-105 + -30x) + 7x * (7 + 2x) + 4x2 * (7 + 2x)) = 0 X(-105 + -30x + (7 * 7x + 2x * 7x) + 4x2 * (7 + 2x)) = 0 X(-105 + -30x + (49x + 14x2) + 4x2 * (7 + 2x)) = 0 X(-105 + -30x + 49x + 14x2 + (7 * 4x2 + 2x * 4x2)) = 0 X(-105 + -30x + 49x + 14x2 + (28x2 + 8x3)) = 0 Combine like terms: -30x + 49x = 19x X(-105 + 19x + 14x2 + 28x2 + 8x3) = 0 Combine like terms: 14x2 + 28x2 = 42x2 X(-105 + 19x + 42x2 + 8x3) = 0 (-105 * X + 19x * X + 42x2 * X + 8x3 * X) = 0 (-105X + 19xX + 42x2X + 8x3X) = 0 Solving -105X + 19xX + 42x2X + 8x3X = 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(-105 + 19x + 42x2 + 8x3) = 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 '(-105 + 19x + 42x2 + 8x3)' equal to zero and attempt to solve: Simplifying -105 + 19x + 42x2 + 8x3 = 0 Solving -105 + 19x + 42x2 + 8x3 = 0 Move all terms containing X to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 19x + 42x2 + 105 + 8x3 = 0 + 105 Reorder the terms: -105 + 105 + 19x + 42x2 + 8x3 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 19x + 42x2 + 8x3 = 0 + 105 19x + 42x2 + 8x3 = 0 + 105 Combine like terms: 0 + 105 = 105 19x + 42x2 + 8x3 = 105 Add '-19x' to each side of the equation. 19x + 42x2 + -19x + 8x3 = 105 + -19x Reorder the terms: 19x + -19x + 42x2 + 8x3 = 105 + -19x Combine like terms: 19x + -19x = 0 0 + 42x2 + 8x3 = 105 + -19x 42x2 + 8x3 = 105 + -19x Add '-42x2' to each side of the equation. 42x2 + -42x2 + 8x3 = 105 + -19x + -42x2 Combine like terms: 42x2 + -42x2 = 0 0 + 8x3 = 105 + -19x + -42x2 8x3 = 105 + -19x + -42x2 Add '-8x3' to each side of the equation. 8x3 + -8x3 = 105 + -19x + -42x2 + -8x3 Combine like terms: 8x3 + -8x3 = 0 0 = 105 + -19x + -42x2 + -8x3 Simplifying 0 = 105 + -19x + -42x2 + -8x3 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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