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Simplifying kxab + mxac + nxad = (10a)(7b + 4c + -6d) Remove parenthesis around (10a) abkx + acmx + adnx = 10a(7b + 4c + -6d) abkx + acmx + adnx = (7b * 10a + 4c * 10a + -6d * 10a) abkx + acmx + adnx = (70ab + 40ac + -60ad) Solving abkx + acmx + adnx = 70ab + 40ac + -60ad Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-70ab' to each side of the equation. abkx + acmx + -70ab + adnx = 70ab + 40ac + -70ab + -60ad Reorder the terms: -70ab + abkx + acmx + adnx = 70ab + 40ac + -70ab + -60ad Reorder the terms: -70ab + abkx + acmx + adnx = 70ab + -70ab + 40ac + -60ad Combine like terms: 70ab + -70ab = 0 -70ab + abkx + acmx + adnx = 0 + 40ac + -60ad -70ab + abkx + acmx + adnx = 40ac + -60ad Add '-40ac' to each side of the equation. -70ab + abkx + acmx + -40ac + adnx = 40ac + -40ac + -60ad Reorder the terms: -70ab + abkx + -40ac + acmx + adnx = 40ac + -40ac + -60ad Combine like terms: 40ac + -40ac = 0 -70ab + abkx + -40ac + acmx + adnx = 0 + -60ad -70ab + abkx + -40ac + acmx + adnx = -60ad Add '60ad' to each side of the equation. -70ab + abkx + -40ac + acmx + 60ad + adnx = -60ad + 60ad Combine like terms: -60ad + 60ad = 0 -70ab + abkx + -40ac + acmx + 60ad + adnx = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-70b + bkx + -40c + cmx + 60d + dnx) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-70b + bkx + -40c + cmx + 60d + dnx)' equal to zero and attempt to solve: Simplifying -70b + bkx + -40c + cmx + 60d + dnx = 0 Solving -70b + bkx + -40c + cmx + 60d + dnx = 0 Move all terms containing a to the left, all other terms to the right. Add '70b' to each side of the equation. -70b + bkx + -40c + cmx + 60d + 70b + dnx = 0 + 70b Reorder the terms: -70b + 70b + bkx + -40c + cmx + 60d + dnx = 0 + 70b Combine like terms: -70b + 70b = 0 0 + bkx + -40c + cmx + 60d + dnx = 0 + 70b bkx + -40c + cmx + 60d + dnx = 0 + 70b Remove the zero: bkx + -40c + cmx + 60d + dnx = 70b Add '-1bkx' to each side of the equation. bkx + -40c + cmx + 60d + -1bkx + dnx = 70b + -1bkx Reorder the terms: bkx + -1bkx + -40c + cmx + 60d + dnx = 70b + -1bkx Combine like terms: bkx + -1bkx = 0 0 + -40c + cmx + 60d + dnx = 70b + -1bkx -40c + cmx + 60d + dnx = 70b + -1bkx Add '40c' to each side of the equation. -40c + cmx + 60d + 40c + dnx = 70b + -1bkx + 40c Reorder the terms: -40c + 40c + cmx + 60d + dnx = 70b + -1bkx + 40c Combine like terms: -40c + 40c = 0 0 + cmx + 60d + dnx = 70b + -1bkx + 40c cmx + 60d + dnx = 70b + -1bkx + 40c Add '-1cmx' to each side of the equation. cmx + 60d + -1cmx + dnx = 70b + -1bkx + 40c + -1cmx Reorder the terms: cmx + -1cmx + 60d + dnx = 70b + -1bkx + 40c + -1cmx Combine like terms: cmx + -1cmx = 0 0 + 60d + dnx = 70b + -1bkx + 40c + -1cmx 60d + dnx = 70b + -1bkx + 40c + -1cmx Add '-60d' to each side of the equation. 60d + -60d + dnx = 70b + -1bkx + 40c + -1cmx + -60d Combine like terms: 60d + -60d = 0 0 + dnx = 70b + -1bkx + 40c + -1cmx + -60d dnx = 70b + -1bkx + 40c + -1cmx + -60d Add '-1dnx' to each side of the equation. dnx + -1dnx = 70b + -1bkx + 40c + -1cmx + -60d + -1dnx Combine like terms: dnx + -1dnx = 0 0 = 70b + -1bkx + 40c + -1cmx + -60d + -1dnx Simplifying 0 = 70b + -1bkx + 40c + -1cmx + -60d + -1dnx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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