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Simplifying (2a + 4)(3a + -5) = 0 Reorder the terms: (4 + 2a)(3a + -5) = 0 Reorder the terms: (4 + 2a)(-5 + 3a) = 0 Multiply (4 + 2a) * (-5 + 3a) (4(-5 + 3a) + 2a * (-5 + 3a)) = 0 ((-5 * 4 + 3a * 4) + 2a * (-5 + 3a)) = 0 ((-20 + 12a) + 2a * (-5 + 3a)) = 0 (-20 + 12a + (-5 * 2a + 3a * 2a)) = 0 (-20 + 12a + (-10a + 6a2)) = 0 Combine like terms: 12a + -10a = 2a (-20 + 2a + 6a2) = 0 Solving -20 + 2a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + a + 3a2) = 0 Factor a trinomial. 2((-2 + -1a)(5 + -3a)) = 0 Ignore the factor 2.Subproblem 1
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 = -2Subproblem 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 = {-2, 1.666666667}
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