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Simplifying (a + 24)(a + -27) = 0 Reorder the terms: (24 + a)(a + -27) = 0 Reorder the terms: (24 + a)(-27 + a) = 0 Multiply (24 + a) * (-27 + a) (24(-27 + a) + a(-27 + a)) = 0 ((-27 * 24 + a * 24) + a(-27 + a)) = 0 ((-648 + 24a) + a(-27 + a)) = 0 (-648 + 24a + (-27 * a + a * a)) = 0 (-648 + 24a + (-27a + a2)) = 0 Combine like terms: 24a + -27a = -3a (-648 + -3a + a2) = 0 Solving -648 + -3a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-24 + -1a)(27 + -1a) = 0Subproblem 1
Set the factor '(-24 + -1a)' equal to zero and attempt to solve: Simplifying -24 + -1a = 0 Solving -24 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -1a = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1a = 0 + 24 -1a = 0 + 24 Combine like terms: 0 + 24 = 24 -1a = 24 Divide each side by '-1'. a = -24 Simplifying a = -24Subproblem 2
Set the factor '(27 + -1a)' equal to zero and attempt to solve: Simplifying 27 + -1a = 0 Solving 27 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1a = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1a = 0 + -27 -1a = 0 + -27 Combine like terms: 0 + -27 = -27 -1a = -27 Divide each side by '-1'. a = 27 Simplifying a = 27Solution
a = {-24, 27}
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