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Simplifying (2a + 5)(a + -4) = 0 Reorder the terms: (5 + 2a)(a + -4) = 0 Reorder the terms: (5 + 2a)(-4 + a) = 0 Multiply (5 + 2a) * (-4 + a) (5(-4 + a) + 2a * (-4 + a)) = 0 ((-4 * 5 + a * 5) + 2a * (-4 + a)) = 0 ((-20 + 5a) + 2a * (-4 + a)) = 0 (-20 + 5a + (-4 * 2a + a * 2a)) = 0 (-20 + 5a + (-8a + 2a2)) = 0 Combine like terms: 5a + -8a = -3a (-20 + -3a + 2a2) = 0 Solving -20 + -3a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -2a)(4 + -1a) = 0Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve: Simplifying -5 + -2a = 0 Solving -5 + -2a = 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 + -2a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2a = 0 + 5 -2a = 0 + 5 Combine like terms: 0 + 5 = 5 -2a = 5 Divide each side by '-2'. a = -2.5 Simplifying a = -2.5Subproblem 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 = {-2.5, 4}
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