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Simplifying (8a + -9)(3a + -4) = 0 Reorder the terms: (-9 + 8a)(3a + -4) = 0 Reorder the terms: (-9 + 8a)(-4 + 3a) = 0 Multiply (-9 + 8a) * (-4 + 3a) (-9(-4 + 3a) + 8a * (-4 + 3a)) = 0 ((-4 * -9 + 3a * -9) + 8a * (-4 + 3a)) = 0 ((36 + -27a) + 8a * (-4 + 3a)) = 0 (36 + -27a + (-4 * 8a + 3a * 8a)) = 0 (36 + -27a + (-32a + 24a2)) = 0 Combine like terms: -27a + -32a = -59a (36 + -59a + 24a2) = 0 Solving 36 + -59a + 24a2 = 0 Solving for variable 'a'. Factor a trinomial. (9 + -8a)(4 + -3a) = 0Subproblem 1
Set the factor '(9 + -8a)' equal to zero and attempt to solve: Simplifying 9 + -8a = 0 Solving 9 + -8a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -8a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8a = 0 + -9 -8a = 0 + -9 Combine like terms: 0 + -9 = -9 -8a = -9 Divide each side by '-8'. a = 1.125 Simplifying a = 1.125Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 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 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Solution
a = {1.125, 1.333333333}
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