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Simplifying 4ab + -24cd + 12ac + -8bd = 0 Reorder the terms: 4ab + 12ac + -8bd + -24cd = 0 Solving 4ab + 12ac + -8bd + -24cd = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8bd' to each side of the equation. 4ab + 12ac + -8bd + 8bd + -24cd = 0 + 8bd Combine like terms: -8bd + 8bd = 0 4ab + 12ac + 0 + -24cd = 0 + 8bd 4ab + 12ac + -24cd = 0 + 8bd Remove the zero: 4ab + 12ac + -24cd = 8bd Add '24cd' to each side of the equation. 4ab + 12ac + -24cd + 24cd = 8bd + 24cd Combine like terms: -24cd + 24cd = 0 4ab + 12ac + 0 = 8bd + 24cd 4ab + 12ac = 8bd + 24cd Reorder the terms: 4ab + 12ac + -8bd + -24cd = 8bd + -8bd + 24cd + -24cd Combine like terms: 8bd + -8bd = 0 4ab + 12ac + -8bd + -24cd = 0 + 24cd + -24cd 4ab + 12ac + -8bd + -24cd = 24cd + -24cd Combine like terms: 24cd + -24cd = 0 4ab + 12ac + -8bd + -24cd = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(ab + 3ac + -2bd + -6cd) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(ab + 3ac + -2bd + -6cd)' equal to zero and attempt to solve: Simplifying ab + 3ac + -2bd + -6cd = 0 Solving ab + 3ac + -2bd + -6cd = 0 Move all terms containing a to the left, all other terms to the right. Add '2bd' to each side of the equation. ab + 3ac + -2bd + 2bd + -6cd = 0 + 2bd Combine like terms: -2bd + 2bd = 0 ab + 3ac + 0 + -6cd = 0 + 2bd ab + 3ac + -6cd = 0 + 2bd Remove the zero: ab + 3ac + -6cd = 2bd Add '6cd' to each side of the equation. ab + 3ac + -6cd + 6cd = 2bd + 6cd Combine like terms: -6cd + 6cd = 0 ab + 3ac + 0 = 2bd + 6cd ab + 3ac = 2bd + 6cd 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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