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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 + -3a)(5 + -2a) = 0Subproblem 1
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 = -1.666666667Subproblem 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 = {-1.666666667, 2.5}
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