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Simplifying (3a + 5)(2a + -4) = 0 Reorder the terms: (5 + 3a)(2a + -4) = 0 Reorder the terms: (5 + 3a)(-4 + 2a) = 0 Multiply (5 + 3a) * (-4 + 2a) (5(-4 + 2a) + 3a * (-4 + 2a)) = 0 ((-4 * 5 + 2a * 5) + 3a * (-4 + 2a)) = 0 ((-20 + 10a) + 3a * (-4 + 2a)) = 0 (-20 + 10a + (-4 * 3a + 2a * 3a)) = 0 (-20 + 10a + (-12a + 6a2)) = 0 Combine like terms: 10a + -12a = -2a (-20 + -2a + 6a2) = 0 Solving -20 + -2a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -1a + 3a2) = 0 Factor a trinomial. 2((-5 + -3a)(2 + -1a)) = 0 Ignore the factor 2.Subproblem 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 '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {-1.666666667, 2}
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