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Simplifying (5a + -2)(-8a + 5) = 0 Reorder the terms: (-2 + 5a)(-8a + 5) = 0 Reorder the terms: (-2 + 5a)(5 + -8a) = 0 Multiply (-2 + 5a) * (5 + -8a) (-2(5 + -8a) + 5a * (5 + -8a)) = 0 ((5 * -2 + -8a * -2) + 5a * (5 + -8a)) = 0 ((-10 + 16a) + 5a * (5 + -8a)) = 0 (-10 + 16a + (5 * 5a + -8a * 5a)) = 0 (-10 + 16a + (25a + -40a2)) = 0 Combine like terms: 16a + 25a = 41a (-10 + 41a + -40a2) = 0 Solving -10 + 41a + -40a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + 8a)(2 + -5a) = 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 + -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 = {0.625, 0.4}
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