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Simplifying 5a8 + -15a7 + -140a6 = 0 Reorder the terms: -140a6 + -15a7 + 5a8 = 0 Solving -140a6 + -15a7 + 5a8 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a6'. 5a6(-28 + -3a + a2) = 0 Factor a trinomial. 5a6((-4 + -1a)(7 + -1a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'a6' equal to zero and attempt to solve: Simplifying a6 = 0 Solving a6 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a6 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-4 + -1a)' equal to zero and attempt to solve: Simplifying -4 + -1a = 0 Solving -4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a = 0 + 4 -1a = 0 + 4 Combine like terms: 0 + 4 = 4 -1a = 4 Divide each side by '-1'. a = -4 Simplifying a = -4Subproblem 3
Set the factor '(7 + -1a)' equal to zero and attempt to solve: Simplifying 7 + -1a = 0 Solving 7 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1a = 0 + -7 -1a = 0 + -7 Combine like terms: 0 + -7 = -7 -1a = -7 Divide each side by '-1'. a = 7 Simplifying a = 7Solution
a = {-4, 7}
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