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Simplifying (3 + -4a)(7 + -5a) = 0 Multiply (3 + -4a) * (7 + -5a) (3(7 + -5a) + -4a * (7 + -5a)) = 0 ((7 * 3 + -5a * 3) + -4a * (7 + -5a)) = 0 ((21 + -15a) + -4a * (7 + -5a)) = 0 (21 + -15a + (7 * -4a + -5a * -4a)) = 0 (21 + -15a + (-28a + 20a2)) = 0 Combine like terms: -15a + -28a = -43a (21 + -43a + 20a2) = 0 Solving 21 + -43a + 20a2 = 0 Solving for variable 'a'. Factor a trinomial. (3 + -4a)(7 + -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 '(7 + -5a)' equal to zero and attempt to solve: Simplifying 7 + -5a = 0 Solving 7 + -5a = 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 + -5a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5a = 0 + -7 -5a = 0 + -7 Combine like terms: 0 + -7 = -7 -5a = -7 Divide each side by '-5'. a = 1.4 Simplifying a = 1.4Solution
a = {0.75, 1.4}
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