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Simplifying (3a + 5)(2a + -3) = 0 Reorder the terms: (5 + 3a)(2a + -3) = 0 Reorder the terms: (5 + 3a)(-3 + 2a) = 0 Multiply (5 + 3a) * (-3 + 2a) (5(-3 + 2a) + 3a * (-3 + 2a)) = 0 ((-3 * 5 + 2a * 5) + 3a * (-3 + 2a)) = 0 ((-15 + 10a) + 3a * (-3 + 2a)) = 0 (-15 + 10a + (-3 * 3a + 2a * 3a)) = 0 (-15 + 10a + (-9a + 6a2)) = 0 Combine like terms: 10a + -9a = 1a (-15 + 1a + 6a2) = 0 Solving -15 + 1a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -3a)(3 + -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 '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {-1.666666667, 1.5}
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