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Simplifying (2a + 3)(a + -5) = 0 Reorder the terms: (3 + 2a)(a + -5) = 0 Reorder the terms: (3 + 2a)(-5 + a) = 0 Multiply (3 + 2a) * (-5 + a) (3(-5 + a) + 2a * (-5 + a)) = 0 ((-5 * 3 + a * 3) + 2a * (-5 + a)) = 0 ((-15 + 3a) + 2a * (-5 + a)) = 0 (-15 + 3a + (-5 * 2a + a * 2a)) = 0 (-15 + 3a + (-10a + 2a2)) = 0 Combine like terms: 3a + -10a = -7a (-15 + -7a + 2a2) = 0 Solving -15 + -7a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -2a)(5 + -1a) = 0Subproblem 1
Set the factor '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 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 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 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 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5Solution
a = {-1.5, 5}
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