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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. (-7 + -3a)(2 + -1a) = 0Subproblem 1
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 = -2.333333333Subproblem 2
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 = 2Solution
a = {-2.333333333, 2}
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