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