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Simplifying 6a(4a + 3) + -5(4a + 3) = 0 Reorder the terms: 6a(3 + 4a) + -5(4a + 3) = 0 (3 * 6a + 4a * 6a) + -5(4a + 3) = 0 (18a + 24a2) + -5(4a + 3) = 0 Reorder the terms: 18a + 24a2 + -5(3 + 4a) = 0 18a + 24a2 + (3 * -5 + 4a * -5) = 0 18a + 24a2 + (-15 + -20a) = 0 Reorder the terms: -15 + 18a + -20a + 24a2 = 0 Combine like terms: 18a + -20a = -2a -15 + -2a + 24a2 = 0 Solving -15 + -2a + 24a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -4a)(5 + -6a) = 0Subproblem 1
Set the factor '(-3 + -4a)' equal to zero and attempt to solve: Simplifying -3 + -4a = 0 Solving -3 + -4a = 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 + -4a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4a = 0 + 3 -4a = 0 + 3 Combine like terms: 0 + 3 = 3 -4a = 3 Divide each side by '-4'. a = -0.75 Simplifying a = -0.75Subproblem 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 = {-0.75, 0.8333333333}
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