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Simplifying (a + 5)(a + -2) = 0 Reorder the terms: (5 + a)(a + -2) = 0 Reorder the terms: (5 + a)(-2 + a) = 0 Multiply (5 + a) * (-2 + a) (5(-2 + a) + a(-2 + a)) = 0 ((-2 * 5 + a * 5) + a(-2 + a)) = 0 ((-10 + 5a) + a(-2 + a)) = 0 (-10 + 5a + (-2 * a + a * a)) = 0 (-10 + 5a + (-2a + a2)) = 0 Combine like terms: 5a + -2a = 3a (-10 + 3a + a2) = 0 Solving -10 + 3a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -1a)(2 + -1a) = 0Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve: Simplifying -5 + -1a = 0 Solving -5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1a = 0 + 5 -1a = 0 + 5 Combine like terms: 0 + 5 = 5 -1a = 5 Divide each side by '-1'. a = -5 Simplifying a = -5Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {-5, 2}
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