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Simplifying (a3 + -2a2)(3a2 + -4a3) = 0 Reorder the terms: (-2a2 + a3)(3a2 + -4a3) = 0 Multiply (-2a2 + a3) * (3a2 + -4a3) (-2a2 * (3a2 + -4a3) + a3(3a2 + -4a3)) = 0 ((3a2 * -2a2 + -4a3 * -2a2) + a3(3a2 + -4a3)) = 0 ((-6a4 + 8a5) + a3(3a2 + -4a3)) = 0 (-6a4 + 8a5 + (3a2 * a3 + -4a3 * a3)) = 0 (-6a4 + 8a5 + (3a5 + -4a6)) = 0 Combine like terms: 8a5 + 3a5 = 11a5 (-6a4 + 11a5 + -4a6) = 0 Solving -6a4 + 11a5 + -4a6 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a4'. a4(-6 + 11a + -4a2) = 0 Factor a trinomial. a4((-2 + a)(3 + -4a)) = 0Subproblem 1
Set the factor 'a4' equal to zero and attempt to solve: Simplifying a4 = 0 Solving a4 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a4 = 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 '(-2 + a)' equal to zero and attempt to solve: Simplifying -2 + a = 0 Solving -2 + a = 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 + a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + a = 0 + 2 a = 0 + 2 Combine like terms: 0 + 2 = 2 a = 2 Simplifying a = 2Subproblem 3
Set the factor '(3 + -4a)' equal to zero and attempt to solve: Simplifying 3 + -4a = 0 Solving 3 + -4a = 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 + -4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a = 0 + -3 -4a = 0 + -3 Combine like terms: 0 + -3 = -3 -4a = -3 Divide each side by '-4'. a = 0.75 Simplifying a = 0.75Solution
a = {2, 0.75}
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