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Simplifying (a + 3)(a + -7) = 0 Reorder the terms: (3 + a)(a + -7) = 0 Reorder the terms: (3 + a)(-7 + a) = 0 Multiply (3 + a) * (-7 + a) (3(-7 + a) + a(-7 + a)) = 0 ((-7 * 3 + a * 3) + a(-7 + a)) = 0 ((-21 + 3a) + a(-7 + a)) = 0 (-21 + 3a + (-7 * a + a * a)) = 0 (-21 + 3a + (-7a + a2)) = 0 Combine like terms: 3a + -7a = -4a (-21 + -4a + a2) = 0 Solving -21 + -4a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -1a)(7 + -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 '(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 = {-3, 7}
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