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Simplifying (a + -4)(a + -5) = 0 Reorder the terms: (-4 + a)(a + -5) = 0 Reorder the terms: (-4 + a)(-5 + a) = 0 Multiply (-4 + a) * (-5 + a) (-4(-5 + a) + a(-5 + a)) = 0 ((-5 * -4 + a * -4) + a(-5 + a)) = 0 ((20 + -4a) + a(-5 + a)) = 0 (20 + -4a + (-5 * a + a * a)) = 0 (20 + -4a + (-5a + a2)) = 0 Combine like terms: -4a + -5a = -9a (20 + -9a + a2) = 0 Solving 20 + -9a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + -1a)(5 + -1a) = 0Subproblem 1
Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4Subproblem 2
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 = 5Solution
a = {4, 5}
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