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Simplifying (a + 5)(a + -8) = 0 Reorder the terms: (5 + a)(a + -8) = 0 Reorder the terms: (5 + a)(-8 + a) = 0 Multiply (5 + a) * (-8 + a) (5(-8 + a) + a(-8 + a)) = 0 ((-8 * 5 + a * 5) + a(-8 + a)) = 0 ((-40 + 5a) + a(-8 + a)) = 0 (-40 + 5a + (-8 * a + a * a)) = 0 (-40 + 5a + (-8a + a2)) = 0 Combine like terms: 5a + -8a = -3a (-40 + -3a + a2) = 0 Solving -40 + -3a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -1a)(8 + -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 '(8 + -1a)' equal to zero and attempt to solve: Simplifying 8 + -1a = 0 Solving 8 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1a = 0 + -8 -1a = 0 + -8 Combine like terms: 0 + -8 = -8 -1a = -8 Divide each side by '-1'. a = 8 Simplifying a = 8Solution
a = {-5, 8}
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