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Simplifying (3a + -5)(3a + 4) = 0 Reorder the terms: (-5 + 3a)(3a + 4) = 0 Reorder the terms: (-5 + 3a)(4 + 3a) = 0 Multiply (-5 + 3a) * (4 + 3a) (-5(4 + 3a) + 3a * (4 + 3a)) = 0 ((4 * -5 + 3a * -5) + 3a * (4 + 3a)) = 0 ((-20 + -15a) + 3a * (4 + 3a)) = 0 (-20 + -15a + (4 * 3a + 3a * 3a)) = 0 (-20 + -15a + (12a + 9a2)) = 0 Combine like terms: -15a + 12a = -3a (-20 + -3a + 9a2) = 0 Solving -20 + -3a + 9a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -3a)(5 + -3a) = 0Subproblem 1
Set the factor '(-4 + -3a)' equal to zero and attempt to solve: Simplifying -4 + -3a = 0 Solving -4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3a = 0 + 4 -3a = 0 + 4 Combine like terms: 0 + 4 = 4 -3a = 4 Divide each side by '-3'. a = -1.333333333 Simplifying a = -1.333333333Subproblem 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 = {-1.333333333, 1.666666667}
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