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Simplifying (a + 3)(a + -12) = 0 Reorder the terms: (3 + a)(a + -12) = 0 Reorder the terms: (3 + a)(-12 + a) = 0 Multiply (3 + a) * (-12 + a) (3(-12 + a) + a(-12 + a)) = 0 ((-12 * 3 + a * 3) + a(-12 + a)) = 0 ((-36 + 3a) + a(-12 + a)) = 0 (-36 + 3a + (-12 * a + a * a)) = 0 (-36 + 3a + (-12a + a2)) = 0 Combine like terms: 3a + -12a = -9a (-36 + -9a + a2) = 0 Solving -36 + -9a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -1a)(12 + -1a) = 0Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3Subproblem 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 = {-3, 12}
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