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Simplifying (3a + -5)(6a + 7) = 0 Reorder the terms: (-5 + 3a)(6a + 7) = 0 Reorder the terms: (-5 + 3a)(7 + 6a) = 0 Multiply (-5 + 3a) * (7 + 6a) (-5(7 + 6a) + 3a * (7 + 6a)) = 0 ((7 * -5 + 6a * -5) + 3a * (7 + 6a)) = 0 ((-35 + -30a) + 3a * (7 + 6a)) = 0 (-35 + -30a + (7 * 3a + 6a * 3a)) = 0 (-35 + -30a + (21a + 18a2)) = 0 Combine like terms: -30a + 21a = -9a (-35 + -9a + 18a2) = 0 Solving -35 + -9a + 18a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -6a)(5 + -3a) = 0Subproblem 1
Set the factor '(-7 + -6a)' equal to zero and attempt to solve: Simplifying -7 + -6a = 0 Solving -7 + -6a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -6a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6a = 0 + 7 -6a = 0 + 7 Combine like terms: 0 + 7 = 7 -6a = 7 Divide each side by '-6'. a = -1.166666667 Simplifying a = -1.166666667Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 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 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Solution
a = {-1.166666667, 1.666666667}
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