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Simplifying (a + 3)(a + -4) = 0 Reorder the terms: (3 + a)(a + -4) = 0 Reorder the terms: (3 + a)(-4 + a) = 0 Multiply (3 + a) * (-4 + a) (3(-4 + a) + a(-4 + a)) = 0 ((-4 * 3 + a * 3) + a(-4 + a)) = 0 ((-12 + 3a) + a(-4 + a)) = 0 (-12 + 3a + (-4 * a + a * a)) = 0 (-12 + 3a + (-4a + a2)) = 0 Combine like terms: 3a + -4a = -1a (-12 + -1a + a2) = 0 Solving -12 + -1a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -1a)(4 + -1a) = 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 '(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 = 4Solution
a = {-3, 4}
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