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Simplifying (a + 5)(3a + -2) = 0 Reorder the terms: (5 + a)(3a + -2) = 0 Reorder the terms: (5 + a)(-2 + 3a) = 0 Multiply (5 + a) * (-2 + 3a) (5(-2 + 3a) + a(-2 + 3a)) = 0 ((-2 * 5 + 3a * 5) + a(-2 + 3a)) = 0 ((-10 + 15a) + a(-2 + 3a)) = 0 (-10 + 15a + (-2 * a + 3a * a)) = 0 (-10 + 15a + (-2a + 3a2)) = 0 Combine like terms: 15a + -2a = 13a (-10 + 13a + 3a2) = 0 Solving -10 + 13a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -1a)(2 + -3a) = 0Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve: Simplifying -5 + -1a = 0 Solving -5 + -1a = 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 + -1a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1a = 0 + 5 -1a = 0 + 5 Combine like terms: 0 + 5 = 5 -1a = 5 Divide each side by '-1'. a = -5 Simplifying a = -5Subproblem 2
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 = 0.6666666667Solution
a = {-5, 0.6666666667}
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