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Simplifying (X + -2)(2x + 6)(3x + -4) = 0 Reorder the terms: (-2 + X)(2x + 6)(3x + -4) = 0 Reorder the terms: (-2 + X)(6 + 2x)(3x + -4) = 0 Reorder the terms: (-2 + X)(6 + 2x)(-4 + 3x) = 0 Multiply (-2 + X) * (6 + 2x) (-2(6 + 2x) + X(6 + 2x))(-4 + 3x) = 0 ((6 * -2 + 2x * -2) + X(6 + 2x))(-4 + 3x) = 0 ((-12 + -4x) + X(6 + 2x))(-4 + 3x) = 0 (-12 + -4x + (6 * X + 2x * X))(-4 + 3x) = 0 (-12 + -4x + (6X + 2xX))(-4 + 3x) = 0 Reorder the terms: (-12 + 6X + -4x + 2xX)(-4 + 3x) = 0 (-12 + 6X + -4x + 2xX)(-4 + 3x) = 0 Multiply (-12 + 6X + -4x + 2xX) * (-4 + 3x) (-12(-4 + 3x) + 6X * (-4 + 3x) + -4x * (-4 + 3x) + 2xX * (-4 + 3x)) = 0 ((-4 * -12 + 3x * -12) + 6X * (-4 + 3x) + -4x * (-4 + 3x) + 2xX * (-4 + 3x)) = 0 ((48 + -36x) + 6X * (-4 + 3x) + -4x * (-4 + 3x) + 2xX * (-4 + 3x)) = 0 (48 + -36x + (-4 * 6X + 3x * 6X) + -4x * (-4 + 3x) + 2xX * (-4 + 3x)) = 0 (48 + -36x + (-24X + 18xX) + -4x * (-4 + 3x) + 2xX * (-4 + 3x)) = 0 (48 + -36x + -24X + 18xX + (-4 * -4x + 3x * -4x) + 2xX * (-4 + 3x)) = 0 (48 + -36x + -24X + 18xX + (16x + -12x2) + 2xX * (-4 + 3x)) = 0 (48 + -36x + -24X + 18xX + 16x + -12x2 + (-4 * 2xX + 3x * 2xX)) = 0 (48 + -36x + -24X + 18xX + 16x + -12x2 + (-8xX + 6x2X)) = 0 Reorder the terms: (48 + -24X + -36x + 16x + 18xX + -8xX + -12x2 + 6x2X) = 0 Combine like terms: -36x + 16x = -20x (48 + -24X + -20x + 18xX + -8xX + -12x2 + 6x2X) = 0 Combine like terms: 18xX + -8xX = 10xX (48 + -24X + -20x + 10xX + -12x2 + 6x2X) = 0 Solving 48 + -24X + -20x + 10xX + -12x2 + 6x2X = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -24X + -20x + 10xX + -12x2 + -48 + 6x2X = 0 + -48 Reorder the terms: 48 + -48 + -24X + -20x + 10xX + -12x2 + 6x2X = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -24X + -20x + 10xX + -12x2 + 6x2X = 0 + -48 -24X + -20x + 10xX + -12x2 + 6x2X = 0 + -48 Combine like terms: 0 + -48 = -48 -24X + -20x + 10xX + -12x2 + 6x2X = -48 Add '20x' to each side of the equation. -24X + -20x + 10xX + -12x2 + 20x + 6x2X = -48 + 20x Reorder the terms: -24X + -20x + 20x + 10xX + -12x2 + 6x2X = -48 + 20x Combine like terms: -20x + 20x = 0 -24X + 0 + 10xX + -12x2 + 6x2X = -48 + 20x -24X + 10xX + -12x2 + 6x2X = -48 + 20x Add '12x2' to each side of the equation. -24X + 10xX + -12x2 + 12x2 + 6x2X = -48 + 20x + 12x2 Combine like terms: -12x2 + 12x2 = 0 -24X + 10xX + 0 + 6x2X = -48 + 20x + 12x2 -24X + 10xX + 6x2X = -48 + 20x + 12x2 Reorder the terms: 48 + -24X + -20x + 10xX + -12x2 + 6x2X = -48 + 20x + 12x2 + 48 + -20x + -12x2 Reorder the terms: 48 + -24X + -20x + 10xX + -12x2 + 6x2X = -48 + 48 + 20x + -20x + 12x2 + -12x2 Combine like terms: -48 + 48 = 0 48 + -24X + -20x + 10xX + -12x2 + 6x2X = 0 + 20x + -20x + 12x2 + -12x2 48 + -24X + -20x + 10xX + -12x2 + 6x2X = 20x + -20x + 12x2 + -12x2 Combine like terms: 20x + -20x = 0 48 + -24X + -20x + 10xX + -12x2 + 6x2X = 0 + 12x2 + -12x2 48 + -24X + -20x + 10xX + -12x2 + 6x2X = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 48 + -24X + -20x + 10xX + -12x2 + 6x2X = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -12X + -10x + 5xX + -6x2 + 3x2X) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -12X + -10x + 5xX + -6x2 + 3x2X)' equal to zero and attempt to solve: Simplifying 24 + -12X + -10x + 5xX + -6x2 + 3x2X = 0 Solving 24 + -12X + -10x + 5xX + -6x2 + 3x2X = 0 Move all terms containing X to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -12X + -10x + 5xX + -6x2 + -24 + 3x2X = 0 + -24 Reorder the terms: 24 + -24 + -12X + -10x + 5xX + -6x2 + 3x2X = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -12X + -10x + 5xX + -6x2 + 3x2X = 0 + -24 -12X + -10x + 5xX + -6x2 + 3x2X = 0 + -24 Combine like terms: 0 + -24 = -24 -12X + -10x + 5xX + -6x2 + 3x2X = -24 Add '10x' to each side of the equation. -12X + -10x + 5xX + -6x2 + 10x + 3x2X = -24 + 10x Reorder the terms: -12X + -10x + 10x + 5xX + -6x2 + 3x2X = -24 + 10x Combine like terms: -10x + 10x = 0 -12X + 0 + 5xX + -6x2 + 3x2X = -24 + 10x -12X + 5xX + -6x2 + 3x2X = -24 + 10x Add '6x2' to each side of the equation. -12X + 5xX + -6x2 + 6x2 + 3x2X = -24 + 10x + 6x2 Combine like terms: -6x2 + 6x2 = 0 -12X + 5xX + 0 + 3x2X = -24 + 10x + 6x2 -12X + 5xX + 3x2X = -24 + 10x + 6x2 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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