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Simplifying (3a + 4)(8a + -3) = 0 Reorder the terms: (4 + 3a)(8a + -3) = 0 Reorder the terms: (4 + 3a)(-3 + 8a) = 0 Multiply (4 + 3a) * (-3 + 8a) (4(-3 + 8a) + 3a * (-3 + 8a)) = 0 ((-3 * 4 + 8a * 4) + 3a * (-3 + 8a)) = 0 ((-12 + 32a) + 3a * (-3 + 8a)) = 0 (-12 + 32a + (-3 * 3a + 8a * 3a)) = 0 (-12 + 32a + (-9a + 24a2)) = 0 Combine like terms: 32a + -9a = 23a (-12 + 23a + 24a2) = 0 Solving -12 + 23a + 24a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -3a)(3 + -8a) = 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 '(3 + -8a)' equal to zero and attempt to solve: Simplifying 3 + -8a = 0 Solving 3 + -8a = 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 + -8a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8a = 0 + -3 -8a = 0 + -3 Combine like terms: 0 + -3 = -3 -8a = -3 Divide each side by '-8'. a = 0.375 Simplifying a = 0.375Solution
a = {-1.333333333, 0.375}
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