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Simplifying (5a + 4)(7a + -4) = 0 Reorder the terms: (4 + 5a)(7a + -4) = 0 Reorder the terms: (4 + 5a)(-4 + 7a) = 0 Multiply (4 + 5a) * (-4 + 7a) (4(-4 + 7a) + 5a * (-4 + 7a)) = 0 ((-4 * 4 + 7a * 4) + 5a * (-4 + 7a)) = 0 ((-16 + 28a) + 5a * (-4 + 7a)) = 0 (-16 + 28a + (-4 * 5a + 7a * 5a)) = 0 (-16 + 28a + (-20a + 35a2)) = 0 Combine like terms: 28a + -20a = 8a (-16 + 8a + 35a2) = 0 Solving -16 + 8a + 35a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -5a)(4 + -7a) = 0Subproblem 1
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 = -0.8Subproblem 2
Set the factor '(4 + -7a)' equal to zero and attempt to solve: Simplifying 4 + -7a = 0 Solving 4 + -7a = 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 + -7a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7a = 0 + -4 -7a = 0 + -4 Combine like terms: 0 + -4 = -4 -7a = -4 Divide each side by '-7'. a = 0.5714285714 Simplifying a = 0.5714285714Solution
a = {-0.8, 0.5714285714}
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