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Simplifying (a + 7)(a + -5) = 0 Reorder the terms: (7 + a)(a + -5) = 0 Reorder the terms: (7 + a)(-5 + a) = 0 Multiply (7 + a) * (-5 + a) (7(-5 + a) + a(-5 + a)) = 0 ((-5 * 7 + a * 7) + a(-5 + a)) = 0 ((-35 + 7a) + a(-5 + a)) = 0 (-35 + 7a + (-5 * a + a * a)) = 0 (-35 + 7a + (-5a + a2)) = 0 Combine like terms: 7a + -5a = 2a (-35 + 2a + a2) = 0 Solving -35 + 2a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -1a)(5 + -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 '(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 = {-7, 5}
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