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Simplifying (7a + -6)(2a + -5) = 0 Reorder the terms: (-6 + 7a)(2a + -5) = 0 Reorder the terms: (-6 + 7a)(-5 + 2a) = 0 Multiply (-6 + 7a) * (-5 + 2a) (-6(-5 + 2a) + 7a * (-5 + 2a)) = 0 ((-5 * -6 + 2a * -6) + 7a * (-5 + 2a)) = 0 ((30 + -12a) + 7a * (-5 + 2a)) = 0 (30 + -12a + (-5 * 7a + 2a * 7a)) = 0 (30 + -12a + (-35a + 14a2)) = 0 Combine like terms: -12a + -35a = -47a (30 + -47a + 14a2) = 0 Solving 30 + -47a + 14a2 = 0 Solving for variable 'a'. Factor a trinomial. (6 + -7a)(5 + -2a) = 0Subproblem 1
Set the factor '(6 + -7a)' equal to zero and attempt to solve: Simplifying 6 + -7a = 0 Solving 6 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7a = 0 + -6 -7a = 0 + -6 Combine like terms: 0 + -6 = -6 -7a = -6 Divide each side by '-7'. a = 0.8571428571 Simplifying a = 0.8571428571Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve: Simplifying 5 + -2a = 0 Solving 5 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2a = 0 + -5 -2a = 0 + -5 Combine like terms: 0 + -5 = -5 -2a = -5 Divide each side by '-2'. a = 2.5 Simplifying a = 2.5Solution
a = {0.8571428571, 2.5}
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