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Simplifying (2a + -5)(a + -3) = 0 Reorder the terms: (-5 + 2a)(a + -3) = 0 Reorder the terms: (-5 + 2a)(-3 + a) = 0 Multiply (-5 + 2a) * (-3 + a) (-5(-3 + a) + 2a * (-3 + a)) = 0 ((-3 * -5 + a * -5) + 2a * (-3 + a)) = 0 ((15 + -5a) + 2a * (-3 + a)) = 0 (15 + -5a + (-3 * 2a + a * 2a)) = 0 (15 + -5a + (-6a + 2a2)) = 0 Combine like terms: -5a + -6a = -11a (15 + -11a + 2a2) = 0 Solving 15 + -11a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (5 + -2a)(3 + -1a) = 0Subproblem 1
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 = 2.5Subproblem 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 = {2.5, 3}
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