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Simplifying (5a + 3)(6a + -7) = 0 Reorder the terms: (3 + 5a)(6a + -7) = 0 Reorder the terms: (3 + 5a)(-7 + 6a) = 0 Multiply (3 + 5a) * (-7 + 6a) (3(-7 + 6a) + 5a * (-7 + 6a)) = 0 ((-7 * 3 + 6a * 3) + 5a * (-7 + 6a)) = 0 ((-21 + 18a) + 5a * (-7 + 6a)) = 0 (-21 + 18a + (-7 * 5a + 6a * 5a)) = 0 (-21 + 18a + (-35a + 30a2)) = 0 Combine like terms: 18a + -35a = -17a (-21 + -17a + 30a2) = 0 Solving -21 + -17a + 30a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -5a)(7 + -6a) = 0Subproblem 1
Set the factor '(-3 + -5a)' equal to zero and attempt to solve: Simplifying -3 + -5a = 0 Solving -3 + -5a = 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 + -5a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5a = 0 + 3 -5a = 0 + 3 Combine like terms: 0 + 3 = 3 -5a = 3 Divide each side by '-5'. a = -0.6 Simplifying a = -0.6Subproblem 2
Set the factor '(7 + -6a)' equal to zero and attempt to solve: Simplifying 7 + -6a = 0 Solving 7 + -6a = 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 + -6a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6a = 0 + -7 -6a = 0 + -7 Combine like terms: 0 + -7 = -7 -6a = -7 Divide each side by '-6'. a = 1.166666667 Simplifying a = 1.166666667Solution
a = {-0.6, 1.166666667}
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