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Simplifying 6a(a + 2) + -5(a + 2) = 0 Reorder the terms: 6a(2 + a) + -5(a + 2) = 0 (2 * 6a + a * 6a) + -5(a + 2) = 0 (12a + 6a2) + -5(a + 2) = 0 Reorder the terms: 12a + 6a2 + -5(2 + a) = 0 12a + 6a2 + (2 * -5 + a * -5) = 0 12a + 6a2 + (-10 + -5a) = 0 Reorder the terms: -10 + 12a + -5a + 6a2 = 0 Combine like terms: 12a + -5a = 7a -10 + 7a + 6a2 = 0 Solving -10 + 7a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (-2 + -1a)(5 + -6a) = 0Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve: Simplifying -2 + -1a = 0 Solving -2 + -1a = 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 + -1a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a = 0 + 2 -1a = 0 + 2 Combine like terms: 0 + 2 = 2 -1a = 2 Divide each side by '-1'. a = -2 Simplifying a = -2Subproblem 2
Set the factor '(5 + -6a)' equal to zero and attempt to solve: Simplifying 5 + -6a = 0 Solving 5 + -6a = 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 + -6a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6a = 0 + -5 -6a = 0 + -5 Combine like terms: 0 + -5 = -5 -6a = -5 Divide each side by '-6'. a = 0.8333333333 Simplifying a = 0.8333333333Solution
a = {-2, 0.8333333333}
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