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Simplifying -3x[-4a + -2x(a + -5)] = -8 + -1[4x(-3a + -1) + -2a] Reorder the terms: -3x[-4a + -2x(-5 + a)] = -8 + -1[4x(-3a + -1) + -2a] -3x[-4a + (-5 * -2x + a * -2x)] = -8 + -1[4x(-3a + -1) + -2a] Reorder the terms: -3x[-4a + (-2ax + 10x)] = -8 + -1[4x(-3a + -1) + -2a] -3x[-4a + (-2ax + 10x)] = -8 + -1[4x(-3a + -1) + -2a] [-4a * -3x + -2ax * -3x + 10x * -3x] = -8 + -1[4x(-3a + -1) + -2a] [12ax + 6ax2 + -30x2] = -8 + -1[4x(-3a + -1) + -2a] Reorder the terms: 12ax + 6ax2 + -30x2 = -8 + -1[4x(-1 + -3a) + -2a] 12ax + 6ax2 + -30x2 = -8 + -1[(-1 * 4x + -3a * 4x) + -2a] Reorder the terms: 12ax + 6ax2 + -30x2 = -8 + -1[(-12ax + -4x) + -2a] 12ax + 6ax2 + -30x2 = -8 + -1[(-12ax + -4x) + -2a] Reorder the terms: 12ax + 6ax2 + -30x2 = -8 + -1[-2a + -12ax + -4x] 12ax + 6ax2 + -30x2 = -8 + [-2a * -1 + -12ax * -1 + -4x * -1] 12ax + 6ax2 + -30x2 = -8 + [2a + 12ax + 4x] Add '-12ax' to each side of the equation. 12ax + 6ax2 + -12ax + -30x2 = -8 + 2a + 12ax + -12ax + 4x Reorder the terms: 12ax + -12ax + 6ax2 + -30x2 = -8 + 2a + 12ax + -12ax + 4x Combine like terms: 12ax + -12ax = 0 0 + 6ax2 + -30x2 = -8 + 2a + 12ax + -12ax + 4x 6ax2 + -30x2 = -8 + 2a + 12ax + -12ax + 4x Combine like terms: 12ax + -12ax = 0 6ax2 + -30x2 = -8 + 2a + 0 + 4x 6ax2 + -30x2 = -8 + 2a + 4x Solving 6ax2 + -30x2 = -8 + 2a + 4x Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2a' to each side of the equation. 6ax2 + -2a + -30x2 = -8 + 2a + -2a + 4x Reorder the terms: -2a + 6ax2 + -30x2 = -8 + 2a + -2a + 4x Combine like terms: 2a + -2a = 0 -2a + 6ax2 + -30x2 = -8 + 0 + 4x -2a + 6ax2 + -30x2 = -8 + 4x Add '30x2' to each side of the equation. -2a + 6ax2 + -30x2 + 30x2 = -8 + 4x + 30x2 Combine like terms: -30x2 + 30x2 = 0 -2a + 6ax2 + 0 = -8 + 4x + 30x2 -2a + 6ax2 = -8 + 4x + 30x2 Reorder the terms: 8 + -2a + 6ax2 + -4x + -30x2 = -8 + 4x + 30x2 + 8 + -4x + -30x2 Reorder the terms: 8 + -2a + 6ax2 + -4x + -30x2 = -8 + 8 + 4x + -4x + 30x2 + -30x2 Combine like terms: -8 + 8 = 0 8 + -2a + 6ax2 + -4x + -30x2 = 0 + 4x + -4x + 30x2 + -30x2 8 + -2a + 6ax2 + -4x + -30x2 = 4x + -4x + 30x2 + -30x2 Combine like terms: 4x + -4x = 0 8 + -2a + 6ax2 + -4x + -30x2 = 0 + 30x2 + -30x2 8 + -2a + 6ax2 + -4x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 8 + -2a + 6ax2 + -4x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -1a + 3ax2 + -2x + -15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1a + 3ax2 + -2x + -15x2)' equal to zero and attempt to solve: Simplifying 4 + -1a + 3ax2 + -2x + -15x2 = 0 Solving 4 + -1a + 3ax2 + -2x + -15x2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -1a + 3ax2 + -2x + -4 + -15x2 = 0 + -4 Reorder the terms: 4 + -4 + -1a + 3ax2 + -2x + -15x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a + 3ax2 + -2x + -15x2 = 0 + -4 -1a + 3ax2 + -2x + -15x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1a + 3ax2 + -2x + -15x2 = -4 Add '2x' to each side of the equation. -1a + 3ax2 + -2x + 2x + -15x2 = -4 + 2x Combine like terms: -2x + 2x = 0 -1a + 3ax2 + 0 + -15x2 = -4 + 2x -1a + 3ax2 + -15x2 = -4 + 2x Add '15x2' to each side of the equation. -1a + 3ax2 + -15x2 + 15x2 = -4 + 2x + 15x2 Combine like terms: -15x2 + 15x2 = 0 -1a + 3ax2 + 0 = -4 + 2x + 15x2 -1a + 3ax2 = -4 + 2x + 15x2 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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