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Simplifying (4a + -5)(4a + 7) = 0 Reorder the terms: (-5 + 4a)(4a + 7) = 0 Reorder the terms: (-5 + 4a)(7 + 4a) = 0 Multiply (-5 + 4a) * (7 + 4a) (-5(7 + 4a) + 4a * (7 + 4a)) = 0 ((7 * -5 + 4a * -5) + 4a * (7 + 4a)) = 0 ((-35 + -20a) + 4a * (7 + 4a)) = 0 (-35 + -20a + (7 * 4a + 4a * 4a)) = 0 (-35 + -20a + (28a + 16a2)) = 0 Combine like terms: -20a + 28a = 8a (-35 + 8a + 16a2) = 0 Solving -35 + 8a + 16a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -4a)(5 + -4a) = 0Subproblem 1
Set the factor '(-7 + -4a)' equal to zero and attempt to solve: Simplifying -7 + -4a = 0 Solving -7 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4a = 0 + 7 -4a = 0 + 7 Combine like terms: 0 + 7 = 7 -4a = 7 Divide each side by '-4'. a = -1.75 Simplifying a = -1.75Subproblem 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 = {-1.75, 1.25}
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