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Simplifying (9 + -4a)(7a + 28) = 0 Reorder the terms: (9 + -4a)(28 + 7a) = 0 Multiply (9 + -4a) * (28 + 7a) (9(28 + 7a) + -4a * (28 + 7a)) = 0 ((28 * 9 + 7a * 9) + -4a * (28 + 7a)) = 0 ((252 + 63a) + -4a * (28 + 7a)) = 0 (252 + 63a + (28 * -4a + 7a * -4a)) = 0 (252 + 63a + (-112a + -28a2)) = 0 Combine like terms: 63a + -112a = -49a (252 + -49a + -28a2) = 0 Solving 252 + -49a + -28a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '7'. 7(36 + -7a + -4a2) = 0 Factor a trinomial. 7((9 + -4a)(4 + a)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(9 + -4a)' equal to zero and attempt to solve: Simplifying 9 + -4a = 0 Solving 9 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4a = 0 + -9 -4a = 0 + -9 Combine like terms: 0 + -9 = -9 -4a = -9 Divide each side by '-4'. a = 2.25 Simplifying a = 2.25Subproblem 2
Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 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 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Solution
a = {2.25, -4}
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