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Simplifying (8a + -7)(4a + -3) = 0 Reorder the terms: (-7 + 8a)(4a + -3) = 0 Reorder the terms: (-7 + 8a)(-3 + 4a) = 0 Multiply (-7 + 8a) * (-3 + 4a) (-7(-3 + 4a) + 8a * (-3 + 4a)) = 0 ((-3 * -7 + 4a * -7) + 8a * (-3 + 4a)) = 0 ((21 + -28a) + 8a * (-3 + 4a)) = 0 (21 + -28a + (-3 * 8a + 4a * 8a)) = 0 (21 + -28a + (-24a + 32a2)) = 0 Combine like terms: -28a + -24a = -52a (21 + -52a + 32a2) = 0 Solving 21 + -52a + 32a2 = 0 Solving for variable 'a'. Factor a trinomial. (3 + -4a)(7 + -8a) = 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 '(7 + -8a)' equal to zero and attempt to solve: Simplifying 7 + -8a = 0 Solving 7 + -8a = 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 + -8a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8a = 0 + -7 -8a = 0 + -7 Combine like terms: 0 + -7 = -7 -8a = -7 Divide each side by '-8'. a = 0.875 Simplifying a = 0.875Solution
a = {0.75, 0.875}
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