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Simplifying (5a + -2)(a + 4) = 0 Reorder the terms: (-2 + 5a)(a + 4) = 0 Reorder the terms: (-2 + 5a)(4 + a) = 0 Multiply (-2 + 5a) * (4 + a) (-2(4 + a) + 5a * (4 + a)) = 0 ((4 * -2 + a * -2) + 5a * (4 + a)) = 0 ((-8 + -2a) + 5a * (4 + a)) = 0 (-8 + -2a + (4 * 5a + a * 5a)) = 0 (-8 + -2a + (20a + 5a2)) = 0 Combine like terms: -2a + 20a = 18a (-8 + 18a + 5a2) = 0 Solving -8 + 18a + 5a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -1a)(2 + -5a) = 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 '(2 + -5a)' equal to zero and attempt to solve: Simplifying 2 + -5a = 0 Solving 2 + -5a = 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 + -5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5a = 0 + -2 -5a = 0 + -2 Combine like terms: 0 + -2 = -2 -5a = -2 Divide each side by '-5'. a = 0.4 Simplifying a = 0.4Solution
a = {-4, 0.4}
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