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Simplifying (8a + 3)(5a + -15) = 0 Reorder the terms: (3 + 8a)(5a + -15) = 0 Reorder the terms: (3 + 8a)(-15 + 5a) = 0 Multiply (3 + 8a) * (-15 + 5a) (3(-15 + 5a) + 8a * (-15 + 5a)) = 0 ((-15 * 3 + 5a * 3) + 8a * (-15 + 5a)) = 0 ((-45 + 15a) + 8a * (-15 + 5a)) = 0 (-45 + 15a + (-15 * 8a + 5a * 8a)) = 0 (-45 + 15a + (-120a + 40a2)) = 0 Combine like terms: 15a + -120a = -105a (-45 + -105a + 40a2) = 0 Solving -45 + -105a + 40a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -21a + 8a2) = 0 Factor a trinomial. 5((-3 + -8a)(3 + -1a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -8a)' equal to zero and attempt to solve: Simplifying -3 + -8a = 0 Solving -3 + -8a = 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 + -8a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8a = 0 + 3 -8a = 0 + 3 Combine like terms: 0 + 3 = 3 -8a = 3 Divide each side by '-8'. a = -0.375 Simplifying a = -0.375Subproblem 2
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 = {-0.375, 3}
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