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Simplifying (a + 4)(2a + -5) = 0 Reorder the terms: (4 + a)(2a + -5) = 0 Reorder the terms: (4 + a)(-5 + 2a) = 0 Multiply (4 + a) * (-5 + 2a) (4(-5 + 2a) + a(-5 + 2a)) = 0 ((-5 * 4 + 2a * 4) + a(-5 + 2a)) = 0 ((-20 + 8a) + a(-5 + 2a)) = 0 (-20 + 8a + (-5 * a + 2a * a)) = 0 (-20 + 8a + (-5a + 2a2)) = 0 Combine like terms: 8a + -5a = 3a (-20 + 3a + 2a2) = 0 Solving -20 + 3a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -1a)(5 + -2a) = 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 + -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 = 2.5Solution
a = {-4, 2.5}
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