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Simplifying (a + 9)(a + -12) = 0 Reorder the terms: (9 + a)(a + -12) = 0 Reorder the terms: (9 + a)(-12 + a) = 0 Multiply (9 + a) * (-12 + a) (9(-12 + a) + a(-12 + a)) = 0 ((-12 * 9 + a * 9) + a(-12 + a)) = 0 ((-108 + 9a) + a(-12 + a)) = 0 (-108 + 9a + (-12 * a + a * a)) = 0 (-108 + 9a + (-12a + a2)) = 0 Combine like terms: 9a + -12a = -3a (-108 + -3a + a2) = 0 Solving -108 + -3a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-9 + -1a)(12 + -1a) = 0Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve: Simplifying -9 + -1a = 0 Solving -9 + -1a = 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 + -1a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1a = 0 + 9 -1a = 0 + 9 Combine like terms: 0 + 9 = 9 -1a = 9 Divide each side by '-1'. a = -9 Simplifying a = -9Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve: Simplifying 12 + -1a = 0 Solving 12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1a = 0 + -12 -1a = 0 + -12 Combine like terms: 0 + -12 = -12 -1a = -12 Divide each side by '-1'. a = 12 Simplifying a = 12Solution
a = {-9, 12}
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