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Simplifying (a + 7)(a + -4) = 0 Reorder the terms: (7 + a)(a + -4) = 0 Reorder the terms: (7 + a)(-4 + a) = 0 Multiply (7 + a) * (-4 + a) (7(-4 + a) + a(-4 + a)) = 0 ((-4 * 7 + a * 7) + a(-4 + a)) = 0 ((-28 + 7a) + a(-4 + a)) = 0 (-28 + 7a + (-4 * a + a * a)) = 0 (-28 + 7a + (-4a + a2)) = 0 Combine like terms: 7a + -4a = 3a (-28 + 3a + a2) = 0 Solving -28 + 3a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -1a)(4 + -1a) = 0Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve: Simplifying -7 + -1a = 0 Solving -7 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1a = 0 + 7 -1a = 0 + 7 Combine like terms: 0 + 7 = 7 -1a = 7 Divide each side by '-1'. a = -7 Simplifying a = -7Subproblem 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 = {-7, 4}
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