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Simplifying (a + 10)(a + -12) = 0 Reorder the terms: (10 + a)(a + -12) = 0 Reorder the terms: (10 + a)(-12 + a) = 0 Multiply (10 + a) * (-12 + a) (10(-12 + a) + a(-12 + a)) = 0 ((-12 * 10 + a * 10) + a(-12 + a)) = 0 ((-120 + 10a) + a(-12 + a)) = 0 (-120 + 10a + (-12 * a + a * a)) = 0 (-120 + 10a + (-12a + a2)) = 0 Combine like terms: 10a + -12a = -2a (-120 + -2a + a2) = 0 Solving -120 + -2a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-10 + -1a)(12 + -1a) = 0Subproblem 1
Set the factor '(-10 + -1a)' equal to zero and attempt to solve: Simplifying -10 + -1a = 0 Solving -10 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1a = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1a = 0 + 10 -1a = 0 + 10 Combine like terms: 0 + 10 = 10 -1a = 10 Divide each side by '-1'. a = -10 Simplifying a = -10Subproblem 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 = {-10, 12}
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