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Simplifying (8a + -19)(a + 16) = 0 Reorder the terms: (-19 + 8a)(a + 16) = 0 Reorder the terms: (-19 + 8a)(16 + a) = 0 Multiply (-19 + 8a) * (16 + a) (-19(16 + a) + 8a * (16 + a)) = 0 ((16 * -19 + a * -19) + 8a * (16 + a)) = 0 ((-304 + -19a) + 8a * (16 + a)) = 0 (-304 + -19a + (16 * 8a + a * 8a)) = 0 (-304 + -19a + (128a + 8a2)) = 0 Combine like terms: -19a + 128a = 109a (-304 + 109a + 8a2) = 0 Solving -304 + 109a + 8a2 = 0 Solving for variable 'a'. Factor a trinomial. (-16 + -1a)(19 + -8a) = 0Subproblem 1
Set the factor '(-16 + -1a)' equal to zero and attempt to solve: Simplifying -16 + -1a = 0 Solving -16 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1a = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1a = 0 + 16 -1a = 0 + 16 Combine like terms: 0 + 16 = 16 -1a = 16 Divide each side by '-1'. a = -16 Simplifying a = -16Subproblem 2
Set the factor '(19 + -8a)' equal to zero and attempt to solve: Simplifying 19 + -8a = 0 Solving 19 + -8a = 0 Move all terms containing a to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -8a = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -8a = 0 + -19 -8a = 0 + -19 Combine like terms: 0 + -19 = -19 -8a = -19 Divide each side by '-8'. a = 2.375 Simplifying a = 2.375Solution
a = {-16, 2.375}
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