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Simplifying (2a + 5)(3a + -5) = 0 Reorder the terms: (5 + 2a)(3a + -5) = 0 Reorder the terms: (5 + 2a)(-5 + 3a) = 0 Multiply (5 + 2a) * (-5 + 3a) (5(-5 + 3a) + 2a * (-5 + 3a)) = 0 ((-5 * 5 + 3a * 5) + 2a * (-5 + 3a)) = 0 ((-25 + 15a) + 2a * (-5 + 3a)) = 0 (-25 + 15a + (-5 * 2a + 3a * 2a)) = 0 (-25 + 15a + (-10a + 6a2)) = 0 Combine like terms: 15a + -10a = 5a (-25 + 5a + 6a2) = 0 Solving -25 + 5a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -2a)(5 + -3a) = 0Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 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 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Solution
a = {-2.5, 1.666666667}
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