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Simplifying (13a + 7)(6a + -5) = 0 Reorder the terms: (7 + 13a)(6a + -5) = 0 Reorder the terms: (7 + 13a)(-5 + 6a) = 0 Multiply (7 + 13a) * (-5 + 6a) (7(-5 + 6a) + 13a * (-5 + 6a)) = 0 ((-5 * 7 + 6a * 7) + 13a * (-5 + 6a)) = 0 ((-35 + 42a) + 13a * (-5 + 6a)) = 0 (-35 + 42a + (-5 * 13a + 6a * 13a)) = 0 (-35 + 42a + (-65a + 78a2)) = 0 Combine like terms: 42a + -65a = -23a (-35 + -23a + 78a2) = 0 Solving -35 + -23a + 78a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -13a)(5 + -6a) = 0Subproblem 1
Set the factor '(-7 + -13a)' equal to zero and attempt to solve: Simplifying -7 + -13a = 0 Solving -7 + -13a = 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 + -13a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -13a = 0 + 7 -13a = 0 + 7 Combine like terms: 0 + 7 = 7 -13a = 7 Divide each side by '-13'. a = -0.5384615385 Simplifying a = -0.5384615385Subproblem 2
Set the factor '(5 + -6a)' equal to zero and attempt to solve: Simplifying 5 + -6a = 0 Solving 5 + -6a = 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 + -6a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6a = 0 + -5 -6a = 0 + -5 Combine like terms: 0 + -5 = -5 -6a = -5 Divide each side by '-6'. a = 0.8333333333 Simplifying a = 0.8333333333Solution
a = {-0.5384615385, 0.8333333333}
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