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Simplifying (a + 7)(a + -12) = 0 Reorder the terms: (7 + a)(a + -12) = 0 Reorder the terms: (7 + a)(-12 + a) = 0 Multiply (7 + a) * (-12 + a) (7(-12 + a) + a(-12 + a)) = 0 ((-12 * 7 + a * 7) + a(-12 + a)) = 0 ((-84 + 7a) + a(-12 + a)) = 0 (-84 + 7a + (-12 * a + a * a)) = 0 (-84 + 7a + (-12a + a2)) = 0 Combine like terms: 7a + -12a = -5a (-84 + -5a + a2) = 0 Solving -84 + -5a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -1a)(12 + -1a) = 0Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve: Simplifying -7 + -1a = 0 Solving -7 + -1a = 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 + -1a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1a = 0 + 7 -1a = 0 + 7 Combine like terms: 0 + 7 = 7 -1a = 7 Divide each side by '-1'. a = -7 Simplifying a = -7Subproblem 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 = {-7, 12}
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