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Simplifying (5a + 3)(2a + -5) = 0 Reorder the terms: (3 + 5a)(2a + -5) = 0 Reorder the terms: (3 + 5a)(-5 + 2a) = 0 Multiply (3 + 5a) * (-5 + 2a) (3(-5 + 2a) + 5a * (-5 + 2a)) = 0 ((-5 * 3 + 2a * 3) + 5a * (-5 + 2a)) = 0 ((-15 + 6a) + 5a * (-5 + 2a)) = 0 (-15 + 6a + (-5 * 5a + 2a * 5a)) = 0 (-15 + 6a + (-25a + 10a2)) = 0 Combine like terms: 6a + -25a = -19a (-15 + -19a + 10a2) = 0 Solving -15 + -19a + 10a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -5a)(5 + -2a) = 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 '(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 = {-0.6, 2.5}
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