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Simplifying (a + -7)(a + -2) = 0 Reorder the terms: (-7 + a)(a + -2) = 0 Reorder the terms: (-7 + a)(-2 + a) = 0 Multiply (-7 + a) * (-2 + a) (-7(-2 + a) + a(-2 + a)) = 0 ((-2 * -7 + a * -7) + a(-2 + a)) = 0 ((14 + -7a) + a(-2 + a)) = 0 (14 + -7a + (-2 * a + a * a)) = 0 (14 + -7a + (-2a + a2)) = 0 Combine like terms: -7a + -2a = -9a (14 + -9a + a2) = 0 Solving 14 + -9a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (2 + -1a)(7 + -1a) = 0Subproblem 1
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Subproblem 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 = {2, 7}
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