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Simplifying (4a + -5)(5a + 3) = 0 Reorder the terms: (-5 + 4a)(5a + 3) = 0 Reorder the terms: (-5 + 4a)(3 + 5a) = 0 Multiply (-5 + 4a) * (3 + 5a) (-5(3 + 5a) + 4a * (3 + 5a)) = 0 ((3 * -5 + 5a * -5) + 4a * (3 + 5a)) = 0 ((-15 + -25a) + 4a * (3 + 5a)) = 0 (-15 + -25a + (3 * 4a + 5a * 4a)) = 0 (-15 + -25a + (12a + 20a2)) = 0 Combine like terms: -25a + 12a = -13a (-15 + -13a + 20a2) = 0 Solving -15 + -13a + 20a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -5a)(5 + -4a) = 0Subproblem 1
Set the factor '(-3 + -5a)' equal to zero and attempt to solve: Simplifying -3 + -5a = 0 Solving -3 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5a = 0 + 3 -5a = 0 + 3 Combine like terms: 0 + 3 = 3 -5a = 3 Divide each side by '-5'. a = -0.6 Simplifying a = -0.6Subproblem 2
Set the factor '(5 + -4a)' equal to zero and attempt to solve: Simplifying 5 + -4a = 0 Solving 5 + -4a = 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 + -4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4a = 0 + -5 -4a = 0 + -5 Combine like terms: 0 + -5 = -5 -4a = -5 Divide each side by '-4'. a = 1.25 Simplifying a = 1.25Solution
a = {-0.6, 1.25}
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