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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. (-5 + -3a)(4 + -3a) = 0Subproblem 1
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 = -1.666666667Subproblem 2
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 = 1.333333333Solution
a = {-1.666666667, 1.333333333}
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