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Simplifying (a3 + -2a2) + -1(3a2 + 4a3) = 0 Reorder the terms: (-2a2 + a3) + -1(3a2 + 4a3) = 0 Remove parenthesis around (-2a2 + a3) -2a2 + a3 + -1(3a2 + 4a3) = 0 -2a2 + a3 + (3a2 * -1 + 4a3 * -1) = 0 -2a2 + a3 + (-3a2 + -4a3) = 0 Reorder the terms: -2a2 + -3a2 + a3 + -4a3 = 0 Combine like terms: -2a2 + -3a2 = -5a2 -5a2 + a3 + -4a3 = 0 Combine like terms: a3 + -4a3 = -3a3 -5a2 + -3a3 = 0 Solving -5a2 + -3a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1a2'. -1a2(5 + 3a) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve: Simplifying a2 = 0 Solving a2 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2 = 0 Take the square root of each side: a = {0}Subproblem 2
Set the factor '(5 + 3a)' equal to zero and attempt to solve: Simplifying 5 + 3a = 0 Solving 5 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3a = 0 + -5 3a = 0 + -5 Combine like terms: 0 + -5 = -5 3a = -5 Divide each side by '3'. a = -1.666666667 Simplifying a = -1.666666667Solution
a = {0, -1.666666667}
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