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Simplifying (3a + -7)(a + 2) = 0 Reorder the terms: (-7 + 3a)(a + 2) = 0 Reorder the terms: (-7 + 3a)(2 + a) = 0 Multiply (-7 + 3a) * (2 + a) (-7(2 + a) + 3a * (2 + a)) = 0 ((2 * -7 + a * -7) + 3a * (2 + a)) = 0 ((-14 + -7a) + 3a * (2 + a)) = 0 (-14 + -7a + (2 * 3a + a * 3a)) = 0 (-14 + -7a + (6a + 3a2)) = 0 Combine like terms: -7a + 6a = -1a (-14 + -1a + 3a2) = 0 Solving -14 + -1a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-2 + -1a)(7 + -3a) = 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 + -3a)' equal to zero and attempt to solve: Simplifying 7 + -3a = 0 Solving 7 + -3a = 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 + -3a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3a = 0 + -7 -3a = 0 + -7 Combine like terms: 0 + -7 = -7 -3a = -7 Divide each side by '-3'. a = 2.333333333 Simplifying a = 2.333333333Solution
a = {-2, 2.333333333}
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