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Simplifying (3a + 6)(5a + -7) = 0 Reorder the terms: (6 + 3a)(5a + -7) = 0 Reorder the terms: (6 + 3a)(-7 + 5a) = 0 Multiply (6 + 3a) * (-7 + 5a) (6(-7 + 5a) + 3a * (-7 + 5a)) = 0 ((-7 * 6 + 5a * 6) + 3a * (-7 + 5a)) = 0 ((-42 + 30a) + 3a * (-7 + 5a)) = 0 (-42 + 30a + (-7 * 3a + 5a * 3a)) = 0 (-42 + 30a + (-21a + 15a2)) = 0 Combine like terms: 30a + -21a = 9a (-42 + 9a + 15a2) = 0 Solving -42 + 9a + 15a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + 3a + 5a2) = 0 Factor a trinomial. 3((-2 + -1a)(7 + -5a)) = 0 Ignore the factor 3.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 '(7 + -5a)' equal to zero and attempt to solve: Simplifying 7 + -5a = 0 Solving 7 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5a = 0 + -7 -5a = 0 + -7 Combine like terms: 0 + -7 = -7 -5a = -7 Divide each side by '-5'. a = 1.4 Simplifying a = 1.4Solution
a = {-2, 1.4}
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