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Simplifying 5(a + 2)(a + -4) = 0 Reorder the terms: 5(2 + a)(a + -4) = 0 Reorder the terms: 5(2 + a)(-4 + a) = 0 Multiply (2 + a) * (-4 + a) 5(2(-4 + a) + a(-4 + a)) = 0 5((-4 * 2 + a * 2) + a(-4 + a)) = 0 5((-8 + 2a) + a(-4 + a)) = 0 5(-8 + 2a + (-4 * a + a * a)) = 0 5(-8 + 2a + (-4a + a2)) = 0 Combine like terms: 2a + -4a = -2a 5(-8 + -2a + a2) = 0 (-8 * 5 + -2a * 5 + a2 * 5) = 0 (-40 + -10a + 5a2) = 0 Solving -40 + -10a + 5a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(-8 + -2a + a2) = 0 Factor a trinomial. 5((-2 + -1a)(4 + -1a)) = 0 Ignore the factor 5.Subproblem 1
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 = -2Subproblem 2
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 = 4Solution
a = {-2, 4}
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