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Simplifying (a + 4)(a + -7) = 0 Reorder the terms: (4 + a)(a + -7) = 0 Reorder the terms: (4 + a)(-7 + a) = 0 Multiply (4 + a) * (-7 + a) (4(-7 + a) + a(-7 + a)) = 0 ((-7 * 4 + a * 4) + a(-7 + a)) = 0 ((-28 + 4a) + a(-7 + a)) = 0 (-28 + 4a + (-7 * a + a * a)) = 0 (-28 + 4a + (-7a + a2)) = 0 Combine like terms: 4a + -7a = -3a (-28 + -3a + a2) = 0 Solving -28 + -3a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -1a)(7 + -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 '(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 = 7Solution
a = {-4, 7}
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