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Simplifying (X + 5)(3x + 6)(2x + -16) = 0 Reorder the terms: (5 + X)(3x + 6)(2x + -16) = 0 Reorder the terms: (5 + X)(6 + 3x)(2x + -16) = 0 Reorder the terms: (5 + X)(6 + 3x)(-16 + 2x) = 0 Multiply (5 + X) * (6 + 3x) (5(6 + 3x) + X(6 + 3x))(-16 + 2x) = 0 ((6 * 5 + 3x * 5) + X(6 + 3x))(-16 + 2x) = 0 ((30 + 15x) + X(6 + 3x))(-16 + 2x) = 0 (30 + 15x + (6 * X + 3x * X))(-16 + 2x) = 0 (30 + 15x + (6X + 3xX))(-16 + 2x) = 0 Reorder the terms: (30 + 6X + 15x + 3xX)(-16 + 2x) = 0 (30 + 6X + 15x + 3xX)(-16 + 2x) = 0 Multiply (30 + 6X + 15x + 3xX) * (-16 + 2x) (30(-16 + 2x) + 6X * (-16 + 2x) + 15x * (-16 + 2x) + 3xX * (-16 + 2x)) = 0 ((-16 * 30 + 2x * 30) + 6X * (-16 + 2x) + 15x * (-16 + 2x) + 3xX * (-16 + 2x)) = 0 ((-480 + 60x) + 6X * (-16 + 2x) + 15x * (-16 + 2x) + 3xX * (-16 + 2x)) = 0 (-480 + 60x + (-16 * 6X + 2x * 6X) + 15x * (-16 + 2x) + 3xX * (-16 + 2x)) = 0 (-480 + 60x + (-96X + 12xX) + 15x * (-16 + 2x) + 3xX * (-16 + 2x)) = 0 (-480 + 60x + -96X + 12xX + (-16 * 15x + 2x * 15x) + 3xX * (-16 + 2x)) = 0 (-480 + 60x + -96X + 12xX + (-240x + 30x2) + 3xX * (-16 + 2x)) = 0 (-480 + 60x + -96X + 12xX + -240x + 30x2 + (-16 * 3xX + 2x * 3xX)) = 0 (-480 + 60x + -96X + 12xX + -240x + 30x2 + (-48xX + 6x2X)) = 0 Reorder the terms: (-480 + -96X + 60x + -240x + 12xX + -48xX + 30x2 + 6x2X) = 0 Combine like terms: 60x + -240x = -180x (-480 + -96X + -180x + 12xX + -48xX + 30x2 + 6x2X) = 0 Combine like terms: 12xX + -48xX = -36xX (-480 + -96X + -180x + -36xX + 30x2 + 6x2X) = 0 Solving -480 + -96X + -180x + -36xX + 30x2 + 6x2X = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '480' to each side of the equation. -480 + -96X + -180x + -36xX + 30x2 + 480 + 6x2X = 0 + 480 Reorder the terms: -480 + 480 + -96X + -180x + -36xX + 30x2 + 6x2X = 0 + 480 Combine like terms: -480 + 480 = 0 0 + -96X + -180x + -36xX + 30x2 + 6x2X = 0 + 480 -96X + -180x + -36xX + 30x2 + 6x2X = 0 + 480 Combine like terms: 0 + 480 = 480 -96X + -180x + -36xX + 30x2 + 6x2X = 480 Add '180x' to each side of the equation. -96X + -180x + -36xX + 30x2 + 180x + 6x2X = 480 + 180x Reorder the terms: -96X + -180x + 180x + -36xX + 30x2 + 6x2X = 480 + 180x Combine like terms: -180x + 180x = 0 -96X + 0 + -36xX + 30x2 + 6x2X = 480 + 180x -96X + -36xX + 30x2 + 6x2X = 480 + 180x Add '-30x2' to each side of the equation. -96X + -36xX + 30x2 + -30x2 + 6x2X = 480 + 180x + -30x2 Combine like terms: 30x2 + -30x2 = 0 -96X + -36xX + 0 + 6x2X = 480 + 180x + -30x2 -96X + -36xX + 6x2X = 480 + 180x + -30x2 Reorder the terms: -480 + -96X + -180x + -36xX + 30x2 + 6x2X = 480 + 180x + -30x2 + -480 + -180x + 30x2 Reorder the terms: -480 + -96X + -180x + -36xX + 30x2 + 6x2X = 480 + -480 + 180x + -180x + -30x2 + 30x2 Combine like terms: 480 + -480 = 0 -480 + -96X + -180x + -36xX + 30x2 + 6x2X = 0 + 180x + -180x + -30x2 + 30x2 -480 + -96X + -180x + -36xX + 30x2 + 6x2X = 180x + -180x + -30x2 + 30x2 Combine like terms: 180x + -180x = 0 -480 + -96X + -180x + -36xX + 30x2 + 6x2X = 0 + -30x2 + 30x2 -480 + -96X + -180x + -36xX + 30x2 + 6x2X = -30x2 + 30x2 Combine like terms: -30x2 + 30x2 = 0 -480 + -96X + -180x + -36xX + 30x2 + 6x2X = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-80 + -16X + -30x + -6xX + 5x2 + x2X) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-80 + -16X + -30x + -6xX + 5x2 + x2X)' equal to zero and attempt to solve: Simplifying -80 + -16X + -30x + -6xX + 5x2 + x2X = 0 Solving -80 + -16X + -30x + -6xX + 5x2 + x2X = 0 Move all terms containing X to the left, all other terms to the right. Add '80' to each side of the equation. -80 + -16X + -30x + -6xX + 5x2 + 80 + x2X = 0 + 80 Reorder the terms: -80 + 80 + -16X + -30x + -6xX + 5x2 + x2X = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -16X + -30x + -6xX + 5x2 + x2X = 0 + 80 -16X + -30x + -6xX + 5x2 + x2X = 0 + 80 Combine like terms: 0 + 80 = 80 -16X + -30x + -6xX + 5x2 + x2X = 80 Add '30x' to each side of the equation. -16X + -30x + -6xX + 5x2 + 30x + x2X = 80 + 30x Reorder the terms: -16X + -30x + 30x + -6xX + 5x2 + x2X = 80 + 30x Combine like terms: -30x + 30x = 0 -16X + 0 + -6xX + 5x2 + x2X = 80 + 30x -16X + -6xX + 5x2 + x2X = 80 + 30x Add '-5x2' to each side of the equation. -16X + -6xX + 5x2 + -5x2 + x2X = 80 + 30x + -5x2 Combine like terms: 5x2 + -5x2 = 0 -16X + -6xX + 0 + x2X = 80 + 30x + -5x2 -16X + -6xX + x2X = 80 + 30x + -5x2 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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