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Simplifying (12a + 7)(5a + -15) = 0 Reorder the terms: (7 + 12a)(5a + -15) = 0 Reorder the terms: (7 + 12a)(-15 + 5a) = 0 Multiply (7 + 12a) * (-15 + 5a) (7(-15 + 5a) + 12a * (-15 + 5a)) = 0 ((-15 * 7 + 5a * 7) + 12a * (-15 + 5a)) = 0 ((-105 + 35a) + 12a * (-15 + 5a)) = 0 (-105 + 35a + (-15 * 12a + 5a * 12a)) = 0 (-105 + 35a + (-180a + 60a2)) = 0 Combine like terms: 35a + -180a = -145a (-105 + -145a + 60a2) = 0 Solving -105 + -145a + 60a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(-21 + -29a + 12a2) = 0 Factor a trinomial. 5((-7 + -12a)(3 + -1a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-7 + -12a)' equal to zero and attempt to solve: Simplifying -7 + -12a = 0 Solving -7 + -12a = 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 + -12a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -12a = 0 + 7 -12a = 0 + 7 Combine like terms: 0 + 7 = 7 -12a = 7 Divide each side by '-12'. a = -0.5833333333 Simplifying a = -0.5833333333Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 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 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-0.5833333333, 3}
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