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Simplifying (2x + 8)(3x + -4f + 6) = 0 Reorder the terms: (8 + 2x)(3x + -4f + 6) = 0 Reorder the terms: (8 + 2x)(6 + -4f + 3x) = 0 Multiply (8 + 2x) * (6 + -4f + 3x) (8(6 + -4f + 3x) + 2x * (6 + -4f + 3x)) = 0 ((6 * 8 + -4f * 8 + 3x * 8) + 2x * (6 + -4f + 3x)) = 0 ((48 + -32f + 24x) + 2x * (6 + -4f + 3x)) = 0 (48 + -32f + 24x + (6 * 2x + -4f * 2x + 3x * 2x)) = 0 Reorder the terms: (48 + -32f + 24x + (-8fx + 12x + 6x2)) = 0 (48 + -32f + 24x + (-8fx + 12x + 6x2)) = 0 Reorder the terms: (48 + -32f + -8fx + 24x + 12x + 6x2) = 0 Combine like terms: 24x + 12x = 36x (48 + -32f + -8fx + 36x + 6x2) = 0 Solving 48 + -32f + -8fx + 36x + 6x2 = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -32f + -8fx + 36x + -48 + 6x2 = 0 + -48 Reorder the terms: 48 + -48 + -32f + -8fx + 36x + 6x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -32f + -8fx + 36x + 6x2 = 0 + -48 -32f + -8fx + 36x + 6x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -32f + -8fx + 36x + 6x2 = -48 Add '-36x' to each side of the equation. -32f + -8fx + 36x + -36x + 6x2 = -48 + -36x Combine like terms: 36x + -36x = 0 -32f + -8fx + 0 + 6x2 = -48 + -36x -32f + -8fx + 6x2 = -48 + -36x Add '-6x2' to each side of the equation. -32f + -8fx + 6x2 + -6x2 = -48 + -36x + -6x2 Combine like terms: 6x2 + -6x2 = 0 -32f + -8fx + 0 = -48 + -36x + -6x2 -32f + -8fx = -48 + -36x + -6x2 Reorder the terms: 48 + -32f + -8fx + 36x + 6x2 = -48 + -36x + -6x2 + 48 + 36x + 6x2 Reorder the terms: 48 + -32f + -8fx + 36x + 6x2 = -48 + 48 + -36x + 36x + -6x2 + 6x2 Combine like terms: -48 + 48 = 0 48 + -32f + -8fx + 36x + 6x2 = 0 + -36x + 36x + -6x2 + 6x2 48 + -32f + -8fx + 36x + 6x2 = -36x + 36x + -6x2 + 6x2 Combine like terms: -36x + 36x = 0 48 + -32f + -8fx + 36x + 6x2 = 0 + -6x2 + 6x2 48 + -32f + -8fx + 36x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 48 + -32f + -8fx + 36x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -16f + -4fx + 18x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -16f + -4fx + 18x + 3x2)' equal to zero and attempt to solve: Simplifying 24 + -16f + -4fx + 18x + 3x2 = 0 Solving 24 + -16f + -4fx + 18x + 3x2 = 0 Move all terms containing f to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -16f + -4fx + 18x + -24 + 3x2 = 0 + -24 Reorder the terms: 24 + -24 + -16f + -4fx + 18x + 3x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -16f + -4fx + 18x + 3x2 = 0 + -24 -16f + -4fx + 18x + 3x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -16f + -4fx + 18x + 3x2 = -24 Add '-18x' to each side of the equation. -16f + -4fx + 18x + -18x + 3x2 = -24 + -18x Combine like terms: 18x + -18x = 0 -16f + -4fx + 0 + 3x2 = -24 + -18x -16f + -4fx + 3x2 = -24 + -18x Add '-3x2' to each side of the equation. -16f + -4fx + 3x2 + -3x2 = -24 + -18x + -3x2 Combine like terms: 3x2 + -3x2 = 0 -16f + -4fx + 0 = -24 + -18x + -3x2 -16f + -4fx = -24 + -18x + -3x2 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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