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Simplifying (2x + 8m)(3a + -4b + 6z) = 0 Reorder the terms: (8m + 2x)(3a + -4b + 6z) = 0 Multiply (8m + 2x) * (3a + -4b + 6z) (8m * (3a + -4b + 6z) + 2x * (3a + -4b + 6z)) = 0 ((3a * 8m + -4b * 8m + 6z * 8m) + 2x * (3a + -4b + 6z)) = 0 ((24am + -32bm + 48mz) + 2x * (3a + -4b + 6z)) = 0 (24am + -32bm + 48mz + (3a * 2x + -4b * 2x + 6z * 2x)) = 0 (24am + -32bm + 48mz + (6ax + -8bx + 12xz)) = 0 Reorder the terms: (24am + 6ax + -32bm + -8bx + 48mz + 12xz) = 0 (24am + 6ax + -32bm + -8bx + 48mz + 12xz) = 0 Solving 24am + 6ax + -32bm + -8bx + 48mz + 12xz = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '32bm' to each side of the equation. 24am + 6ax + -32bm + -8bx + 48mz + 32bm + 12xz = 0 + 32bm Reorder the terms: 24am + 6ax + -32bm + 32bm + -8bx + 48mz + 12xz = 0 + 32bm Combine like terms: -32bm + 32bm = 0 24am + 6ax + 0 + -8bx + 48mz + 12xz = 0 + 32bm 24am + 6ax + -8bx + 48mz + 12xz = 0 + 32bm Remove the zero: 24am + 6ax + -8bx + 48mz + 12xz = 32bm Add '8bx' to each side of the equation. 24am + 6ax + -8bx + 48mz + 8bx + 12xz = 32bm + 8bx Reorder the terms: 24am + 6ax + -8bx + 8bx + 48mz + 12xz = 32bm + 8bx Combine like terms: -8bx + 8bx = 0 24am + 6ax + 0 + 48mz + 12xz = 32bm + 8bx 24am + 6ax + 48mz + 12xz = 32bm + 8bx Add '-48mz' to each side of the equation. 24am + 6ax + 48mz + -48mz + 12xz = 32bm + 8bx + -48mz Combine like terms: 48mz + -48mz = 0 24am + 6ax + 0 + 12xz = 32bm + 8bx + -48mz 24am + 6ax + 12xz = 32bm + 8bx + -48mz Add '-12xz' to each side of the equation. 24am + 6ax + 12xz + -12xz = 32bm + 8bx + -48mz + -12xz Combine like terms: 12xz + -12xz = 0 24am + 6ax + 0 = 32bm + 8bx + -48mz + -12xz 24am + 6ax = 32bm + 8bx + -48mz + -12xz Reorder the terms: 24am + 6ax + -32bm + -8bx + 48mz + 12xz = 32bm + -32bm + 8bx + -8bx + -48mz + 48mz + -12xz + 12xz Combine like terms: 32bm + -32bm = 0 24am + 6ax + -32bm + -8bx + 48mz + 12xz = 0 + 8bx + -8bx + -48mz + 48mz + -12xz + 12xz 24am + 6ax + -32bm + -8bx + 48mz + 12xz = 8bx + -8bx + -48mz + 48mz + -12xz + 12xz Combine like terms: 8bx + -8bx = 0 24am + 6ax + -32bm + -8bx + 48mz + 12xz = 0 + -48mz + 48mz + -12xz + 12xz 24am + 6ax + -32bm + -8bx + 48mz + 12xz = -48mz + 48mz + -12xz + 12xz Combine like terms: -48mz + 48mz = 0 24am + 6ax + -32bm + -8bx + 48mz + 12xz = 0 + -12xz + 12xz 24am + 6ax + -32bm + -8bx + 48mz + 12xz = -12xz + 12xz Combine like terms: -12xz + 12xz = 0 24am + 6ax + -32bm + -8bx + 48mz + 12xz = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12am + 3ax + -16bm + -4bx + 24mz + 6xz) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12am + 3ax + -16bm + -4bx + 24mz + 6xz)' equal to zero and attempt to solve: Simplifying 12am + 3ax + -16bm + -4bx + 24mz + 6xz = 0 Solving 12am + 3ax + -16bm + -4bx + 24mz + 6xz = 0 Move all terms containing a to the left, all other terms to the right. Add '16bm' to each side of the equation. 12am + 3ax + -16bm + -4bx + 24mz + 16bm + 6xz = 0 + 16bm Reorder the terms: 12am + 3ax + -16bm + 16bm + -4bx + 24mz + 6xz = 0 + 16bm Combine like terms: -16bm + 16bm = 0 12am + 3ax + 0 + -4bx + 24mz + 6xz = 0 + 16bm 12am + 3ax + -4bx + 24mz + 6xz = 0 + 16bm Remove the zero: 12am + 3ax + -4bx + 24mz + 6xz = 16bm Add '4bx' to each side of the equation. 12am + 3ax + -4bx + 24mz + 4bx + 6xz = 16bm + 4bx Reorder the terms: 12am + 3ax + -4bx + 4bx + 24mz + 6xz = 16bm + 4bx Combine like terms: -4bx + 4bx = 0 12am + 3ax + 0 + 24mz + 6xz = 16bm + 4bx 12am + 3ax + 24mz + 6xz = 16bm + 4bx Add '-24mz' to each side of the equation. 12am + 3ax + 24mz + -24mz + 6xz = 16bm + 4bx + -24mz Combine like terms: 24mz + -24mz = 0 12am + 3ax + 0 + 6xz = 16bm + 4bx + -24mz 12am + 3ax + 6xz = 16bm + 4bx + -24mz Add '-6xz' to each side of the equation. 12am + 3ax + 6xz + -6xz = 16bm + 4bx + -24mz + -6xz Combine like terms: 6xz + -6xz = 0 12am + 3ax + 0 = 16bm + 4bx + -24mz + -6xz 12am + 3ax = 16bm + 4bx + -24mz + -6xz 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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