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Simplifying (3a + 2)(2a + -5) = 0 Reorder the terms: (2 + 3a)(2a + -5) = 0 Reorder the terms: (2 + 3a)(-5 + 2a) = 0 Multiply (2 + 3a) * (-5 + 2a) (2(-5 + 2a) + 3a * (-5 + 2a)) = 0 ((-5 * 2 + 2a * 2) + 3a * (-5 + 2a)) = 0 ((-10 + 4a) + 3a * (-5 + 2a)) = 0 (-10 + 4a + (-5 * 3a + 2a * 3a)) = 0 (-10 + 4a + (-15a + 6a2)) = 0 Combine like terms: 4a + -15a = -11a (-10 + -11a + 6a2) = 0 Solving -10 + -11a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (-2 + -3a)(5 + -2a) = 0Subproblem 1
Set the factor '(-2 + -3a)' equal to zero and attempt to solve: Simplifying -2 + -3a = 0 Solving -2 + -3a = 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 + -3a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3a = 0 + 2 -3a = 0 + 2 Combine like terms: 0 + 2 = 2 -3a = 2 Divide each side by '-3'. a = -0.6666666667 Simplifying a = -0.6666666667Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve: Simplifying 5 + -2a = 0 Solving 5 + -2a = 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 + -2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2a = 0 + -5 -2a = 0 + -5 Combine like terms: 0 + -5 = -5 -2a = -5 Divide each side by '-2'. a = 2.5 Simplifying a = 2.5Solution
a = {-0.6666666667, 2.5}
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