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Simplifying (8a + -5)(a + -2) = 0 Reorder the terms: (-5 + 8a)(a + -2) = 0 Reorder the terms: (-5 + 8a)(-2 + a) = 0 Multiply (-5 + 8a) * (-2 + a) (-5(-2 + a) + 8a * (-2 + a)) = 0 ((-2 * -5 + a * -5) + 8a * (-2 + a)) = 0 ((10 + -5a) + 8a * (-2 + a)) = 0 (10 + -5a + (-2 * 8a + a * 8a)) = 0 (10 + -5a + (-16a + 8a2)) = 0 Combine like terms: -5a + -16a = -21a (10 + -21a + 8a2) = 0 Solving 10 + -21a + 8a2 = 0 Solving for variable 'a'. Factor a trinomial. (5 + -8a)(2 + -1a) = 0Subproblem 1
Set the factor '(5 + -8a)' equal to zero and attempt to solve: Simplifying 5 + -8a = 0 Solving 5 + -8a = 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 + -8a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8a = 0 + -5 -8a = 0 + -5 Combine like terms: 0 + -5 = -5 -8a = -5 Divide each side by '-8'. a = 0.625 Simplifying a = 0.625Subproblem 2
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 = 2Solution
a = {0.625, 2}
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