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Simplifying (3a + 8)(4a + -5) = 0 Reorder the terms: (8 + 3a)(4a + -5) = 0 Reorder the terms: (8 + 3a)(-5 + 4a) = 0 Multiply (8 + 3a) * (-5 + 4a) (8(-5 + 4a) + 3a * (-5 + 4a)) = 0 ((-5 * 8 + 4a * 8) + 3a * (-5 + 4a)) = 0 ((-40 + 32a) + 3a * (-5 + 4a)) = 0 (-40 + 32a + (-5 * 3a + 4a * 3a)) = 0 (-40 + 32a + (-15a + 12a2)) = 0 Combine like terms: 32a + -15a = 17a (-40 + 17a + 12a2) = 0 Solving -40 + 17a + 12a2 = 0 Solving for variable 'a'. Factor a trinomial. (-8 + -3a)(5 + -4a) = 0Subproblem 1
Set the factor '(-8 + -3a)' equal to zero and attempt to solve: Simplifying -8 + -3a = 0 Solving -8 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3a = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3a = 0 + 8 -3a = 0 + 8 Combine like terms: 0 + 8 = 8 -3a = 8 Divide each side by '-3'. a = -2.666666667 Simplifying a = -2.666666667Subproblem 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 = {-2.666666667, 1.25}
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