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Simplifying (a + 3)(a + -4) = 8 Reorder the terms: (3 + a)(a + -4) = 8 Reorder the terms: (3 + a)(-4 + a) = 8 Multiply (3 + a) * (-4 + a) (3(-4 + a) + a(-4 + a)) = 8 ((-4 * 3 + a * 3) + a(-4 + a)) = 8 ((-12 + 3a) + a(-4 + a)) = 8 (-12 + 3a + (-4 * a + a * a)) = 8 (-12 + 3a + (-4a + a2)) = 8 Combine like terms: 3a + -4a = -1a (-12 + -1a + a2) = 8 Solving -12 + -1a + a2 = 8 Solving for variable 'a'. Reorder the terms: -12 + -8 + -1a + a2 = 8 + -8 Combine like terms: -12 + -8 = -20 -20 + -1a + a2 = 8 + -8 Combine like terms: 8 + -8 = 0 -20 + -1a + a2 = 0 Factor a trinomial. (-4 + -1a)(5 + -1a) = 0Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve: Simplifying -4 + -1a = 0 Solving -4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a = 0 + 4 -1a = 0 + 4 Combine like terms: 0 + 4 = 4 -1a = 4 Divide each side by '-1'. a = -4 Simplifying a = -4Subproblem 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 = {-4, 5}
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