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Simplifying 3x3 + -6x(a + -4) + 12x2 + -18x + 24(a + 5) = 0 Reorder the terms: 3x3 + -6x(-4 + a) + 12x2 + -18x + 24(a + 5) = 0 3x3 + (-4 * -6x + a * -6x) + 12x2 + -18x + 24(a + 5) = 0 Reorder the terms: 3x3 + (-6ax + 24x) + 12x2 + -18x + 24(a + 5) = 0 3x3 + (-6ax + 24x) + 12x2 + -18x + 24(a + 5) = 0 Reorder the terms: 3x3 + -6ax + 24x + 12x2 + -18x + 24(5 + a) = 0 3x3 + -6ax + 24x + 12x2 + -18x + (5 * 24 + a * 24) = 0 3x3 + -6ax + 24x + 12x2 + -18x + (120 + 24a) = 0 Reorder the terms: 120 + 24a + -6ax + 24x + -18x + 12x2 + 3x3 = 0 Combine like terms: 24x + -18x = 6x 120 + 24a + -6ax + 6x + 12x2 + 3x3 = 0 Solving 120 + 24a + -6ax + 6x + 12x2 + 3x3 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + 24a + -6ax + 6x + 12x2 + -120 + 3x3 = 0 + -120 Reorder the terms: 120 + -120 + 24a + -6ax + 6x + 12x2 + 3x3 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 24a + -6ax + 6x + 12x2 + 3x3 = 0 + -120 24a + -6ax + 6x + 12x2 + 3x3 = 0 + -120 Combine like terms: 0 + -120 = -120 24a + -6ax + 6x + 12x2 + 3x3 = -120 Add '-6x' to each side of the equation. 24a + -6ax + 6x + 12x2 + -6x + 3x3 = -120 + -6x Reorder the terms: 24a + -6ax + 6x + -6x + 12x2 + 3x3 = -120 + -6x Combine like terms: 6x + -6x = 0 24a + -6ax + 0 + 12x2 + 3x3 = -120 + -6x 24a + -6ax + 12x2 + 3x3 = -120 + -6x Add '-12x2' to each side of the equation. 24a + -6ax + 12x2 + -12x2 + 3x3 = -120 + -6x + -12x2 Combine like terms: 12x2 + -12x2 = 0 24a + -6ax + 0 + 3x3 = -120 + -6x + -12x2 24a + -6ax + 3x3 = -120 + -6x + -12x2 Add '-3x3' to each side of the equation. 24a + -6ax + 3x3 + -3x3 = -120 + -6x + -12x2 + -3x3 Combine like terms: 3x3 + -3x3 = 0 24a + -6ax + 0 = -120 + -6x + -12x2 + -3x3 24a + -6ax = -120 + -6x + -12x2 + -3x3 Reorder the terms: 120 + 24a + -6ax + 6x + 12x2 + 3x3 = -120 + -6x + -12x2 + -3x3 + 120 + 6x + 12x2 + 3x3 Reorder the terms: 120 + 24a + -6ax + 6x + 12x2 + 3x3 = -120 + 120 + -6x + 6x + -12x2 + 12x2 + -3x3 + 3x3 Combine like terms: -120 + 120 = 0 120 + 24a + -6ax + 6x + 12x2 + 3x3 = 0 + -6x + 6x + -12x2 + 12x2 + -3x3 + 3x3 120 + 24a + -6ax + 6x + 12x2 + 3x3 = -6x + 6x + -12x2 + 12x2 + -3x3 + 3x3 Combine like terms: -6x + 6x = 0 120 + 24a + -6ax + 6x + 12x2 + 3x3 = 0 + -12x2 + 12x2 + -3x3 + 3x3 120 + 24a + -6ax + 6x + 12x2 + 3x3 = -12x2 + 12x2 + -3x3 + 3x3 Combine like terms: -12x2 + 12x2 = 0 120 + 24a + -6ax + 6x + 12x2 + 3x3 = 0 + -3x3 + 3x3 120 + 24a + -6ax + 6x + 12x2 + 3x3 = -3x3 + 3x3 Combine like terms: -3x3 + 3x3 = 0 120 + 24a + -6ax + 6x + 12x2 + 3x3 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(40 + 8a + -2ax + 2x + 4x2 + x3) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(40 + 8a + -2ax + 2x + 4x2 + x3)' equal to zero and attempt to solve: Simplifying 40 + 8a + -2ax + 2x + 4x2 + x3 = 0 Solving 40 + 8a + -2ax + 2x + 4x2 + x3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + 8a + -2ax + 2x + 4x2 + -40 + x3 = 0 + -40 Reorder the terms: 40 + -40 + 8a + -2ax + 2x + 4x2 + x3 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 8a + -2ax + 2x + 4x2 + x3 = 0 + -40 8a + -2ax + 2x + 4x2 + x3 = 0 + -40 Combine like terms: 0 + -40 = -40 8a + -2ax + 2x + 4x2 + x3 = -40 Add '-2x' to each side of the equation. 8a + -2ax + 2x + 4x2 + -2x + x3 = -40 + -2x Reorder the terms: 8a + -2ax + 2x + -2x + 4x2 + x3 = -40 + -2x Combine like terms: 2x + -2x = 0 8a + -2ax + 0 + 4x2 + x3 = -40 + -2x 8a + -2ax + 4x2 + x3 = -40 + -2x Add '-4x2' to each side of the equation. 8a + -2ax + 4x2 + -4x2 + x3 = -40 + -2x + -4x2 Combine like terms: 4x2 + -4x2 = 0 8a + -2ax + 0 + x3 = -40 + -2x + -4x2 8a + -2ax + x3 = -40 + -2x + -4x2 Add '-1x3' to each side of the equation. 8a + -2ax + x3 + -1x3 = -40 + -2x + -4x2 + -1x3 Combine like terms: x3 + -1x3 = 0 8a + -2ax + 0 = -40 + -2x + -4x2 + -1x3 8a + -2ax = -40 + -2x + -4x2 + -1x3 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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