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Simplifying (5a + -4)(4a + 7) = 0 Reorder the terms: (-4 + 5a)(4a + 7) = 0 Reorder the terms: (-4 + 5a)(7 + 4a) = 0 Multiply (-4 + 5a) * (7 + 4a) (-4(7 + 4a) + 5a * (7 + 4a)) = 0 ((7 * -4 + 4a * -4) + 5a * (7 + 4a)) = 0 ((-28 + -16a) + 5a * (7 + 4a)) = 0 (-28 + -16a + (7 * 5a + 4a * 5a)) = 0 (-28 + -16a + (35a + 20a2)) = 0 Combine like terms: -16a + 35a = 19a (-28 + 19a + 20a2) = 0 Solving -28 + 19a + 20a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -4a)(4 + -5a) = 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 '(4 + -5a)' equal to zero and attempt to solve: Simplifying 4 + -5a = 0 Solving 4 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5a = 0 + -4 -5a = 0 + -4 Combine like terms: 0 + -4 = -4 -5a = -4 Divide each side by '-5'. a = 0.8 Simplifying a = 0.8Solution
a = {-1.75, 0.8}
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