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Simplifying (a + 3)(2a + -1) = 0 Reorder the terms: (3 + a)(2a + -1) = 0 Reorder the terms: (3 + a)(-1 + 2a) = 0 Multiply (3 + a) * (-1 + 2a) (3(-1 + 2a) + a(-1 + 2a)) = 0 ((-1 * 3 + 2a * 3) + a(-1 + 2a)) = 0 ((-3 + 6a) + a(-1 + 2a)) = 0 (-3 + 6a + (-1 * a + 2a * a)) = 0 (-3 + 6a + (-1a + 2a2)) = 0 Combine like terms: 6a + -1a = 5a (-3 + 5a + 2a2) = 0 Solving -3 + 5a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -1a)(1 + -2a) = 0Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 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 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {-3, 0.5}
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