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Simplifying a5 + -18a = 7a3 Reorder the terms: -18a + a5 = 7a3 Solving -18a + a5 = 7a3 Solving for variable 'a'. Reorder the terms: -18a + -7a3 + a5 = 7a3 + -7a3 Combine like terms: 7a3 + -7a3 = 0 -18a + -7a3 + a5 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-18 + -7a2 + a4) = 0 Factor a trinomial. a((-2 + -1a2)(9 + -1a2)) = 0 Factor a difference between two squares. a((-2 + -1a2)((3 + a)(3 + -1a))) = 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 '(-2 + -1a2)' equal to zero and attempt to solve: Simplifying -2 + -1a2 = 0 Solving -2 + -1a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a2 = 0 + 2 -1a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1a2 = 2 Divide each side by '-1'. a2 = -2 Simplifying a2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + a)' equal to zero and attempt to solve: Simplifying 3 + a = 0 Solving 3 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0 + -3 a = 0 + -3 Combine like terms: 0 + -3 = -3 a = -3 Simplifying a = -3Subproblem 4
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {0, -3, 3}
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