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Simplifying (3a + -11)(5a + 9) = 0 Reorder the terms: (-11 + 3a)(5a + 9) = 0 Reorder the terms: (-11 + 3a)(9 + 5a) = 0 Multiply (-11 + 3a) * (9 + 5a) (-11(9 + 5a) + 3a * (9 + 5a)) = 0 ((9 * -11 + 5a * -11) + 3a * (9 + 5a)) = 0 ((-99 + -55a) + 3a * (9 + 5a)) = 0 (-99 + -55a + (9 * 3a + 5a * 3a)) = 0 (-99 + -55a + (27a + 15a2)) = 0 Combine like terms: -55a + 27a = -28a (-99 + -28a + 15a2) = 0 Solving -99 + -28a + 15a2 = 0 Solving for variable 'a'. Factor a trinomial. (-9 + -5a)(11 + -3a) = 0Subproblem 1
Set the factor '(-9 + -5a)' equal to zero and attempt to solve: Simplifying -9 + -5a = 0 Solving -9 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -5a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5a = 0 + 9 -5a = 0 + 9 Combine like terms: 0 + 9 = 9 -5a = 9 Divide each side by '-5'. a = -1.8 Simplifying a = -1.8Subproblem 2
Set the factor '(11 + -3a)' equal to zero and attempt to solve: Simplifying 11 + -3a = 0 Solving 11 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -3a = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -3a = 0 + -11 -3a = 0 + -11 Combine like terms: 0 + -11 = -11 -3a = -11 Divide each side by '-3'. a = 3.666666667 Simplifying a = 3.666666667Solution
a = {-1.8, 3.666666667}
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