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Simplifying (a + -3)(3a + 7) = 0 Reorder the terms: (-3 + a)(3a + 7) = 0 Reorder the terms: (-3 + a)(7 + 3a) = 0 Multiply (-3 + a) * (7 + 3a) (-3(7 + 3a) + a(7 + 3a)) = 0 ((7 * -3 + 3a * -3) + a(7 + 3a)) = 0 ((-21 + -9a) + a(7 + 3a)) = 0 (-21 + -9a + (7 * a + 3a * a)) = 0 (-21 + -9a + (7a + 3a2)) = 0 Combine like terms: -9a + 7a = -2a (-21 + -2a + 3a2) = 0 Solving -21 + -2a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -3a)(3 + -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 '(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 = 3Solution
a = {-2.333333333, 3}
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