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Simplifying (3a + 5)(2a + -9) = 0 Reorder the terms: (5 + 3a)(2a + -9) = 0 Reorder the terms: (5 + 3a)(-9 + 2a) = 0 Multiply (5 + 3a) * (-9 + 2a) (5(-9 + 2a) + 3a * (-9 + 2a)) = 0 ((-9 * 5 + 2a * 5) + 3a * (-9 + 2a)) = 0 ((-45 + 10a) + 3a * (-9 + 2a)) = 0 (-45 + 10a + (-9 * 3a + 2a * 3a)) = 0 (-45 + 10a + (-27a + 6a2)) = 0 Combine like terms: 10a + -27a = -17a (-45 + -17a + 6a2) = 0 Solving -45 + -17a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -3a)(9 + -2a) = 0Subproblem 1
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 = -1.666666667Subproblem 2
Set the factor '(9 + -2a)' equal to zero and attempt to solve: Simplifying 9 + -2a = 0 Solving 9 + -2a = 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 + -2a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2a = 0 + -9 -2a = 0 + -9 Combine like terms: 0 + -9 = -9 -2a = -9 Divide each side by '-2'. a = 4.5 Simplifying a = 4.5Solution
a = {-1.666666667, 4.5}
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