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Simplifying (4a + -3)(5a + -4) = 0 Reorder the terms: (-3 + 4a)(5a + -4) = 0 Reorder the terms: (-3 + 4a)(-4 + 5a) = 0 Multiply (-3 + 4a) * (-4 + 5a) (-3(-4 + 5a) + 4a * (-4 + 5a)) = 0 ((-4 * -3 + 5a * -3) + 4a * (-4 + 5a)) = 0 ((12 + -15a) + 4a * (-4 + 5a)) = 0 (12 + -15a + (-4 * 4a + 5a * 4a)) = 0 (12 + -15a + (-16a + 20a2)) = 0 Combine like terms: -15a + -16a = -31a (12 + -31a + 20a2) = 0 Solving 12 + -31a + 20a2 = 0 Solving for variable 'a'. Factor a trinomial. (3 + -4a)(4 + -5a) = 0Subproblem 1
Set the factor '(3 + -4a)' equal to zero and attempt to solve: Simplifying 3 + -4a = 0 Solving 3 + -4a = 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 + -4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a = 0 + -3 -4a = 0 + -3 Combine like terms: 0 + -3 = -3 -4a = -3 Divide each side by '-4'. a = 0.75 Simplifying a = 0.75Subproblem 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 = {0.75, 0.8}
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