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Simplifying (a + -7)(3a + 2) = 0 Reorder the terms: (-7 + a)(3a + 2) = 0 Reorder the terms: (-7 + a)(2 + 3a) = 0 Multiply (-7 + a) * (2 + 3a) (-7(2 + 3a) + a(2 + 3a)) = 0 ((2 * -7 + 3a * -7) + a(2 + 3a)) = 0 ((-14 + -21a) + a(2 + 3a)) = 0 (-14 + -21a + (2 * a + 3a * a)) = 0 (-14 + -21a + (2a + 3a2)) = 0 Combine like terms: -21a + 2a = -19a (-14 + -19a + 3a2) = 0 Solving -14 + -19a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-2 + -3a)(7 + -1a) = 0Subproblem 1
Set the factor '(-2 + -3a)' equal to zero and attempt to solve: Simplifying -2 + -3a = 0 Solving -2 + -3a = 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 + -3a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3a = 0 + 2 -3a = 0 + 2 Combine like terms: 0 + 2 = 2 -3a = 2 Divide each side by '-3'. a = -0.6666666667 Simplifying a = -0.6666666667Subproblem 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 = {-0.6666666667, 7}
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