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Simplifying (6a2 + 3a + -4) + (-3a2 + 2a + 6) = 0 Reorder the terms: (-4 + 3a + 6a2) + (-3a2 + 2a + 6) = 0 Remove parenthesis around (-4 + 3a + 6a2) -4 + 3a + 6a2 + (-3a2 + 2a + 6) = 0 Reorder the terms: -4 + 3a + 6a2 + (6 + 2a + -3a2) = 0 Remove parenthesis around (6 + 2a + -3a2) -4 + 3a + 6a2 + 6 + 2a + -3a2 = 0 Reorder the terms: -4 + 6 + 3a + 2a + 6a2 + -3a2 = 0 Combine like terms: -4 + 6 = 2 2 + 3a + 2a + 6a2 + -3a2 = 0 Combine like terms: 3a + 2a = 5a 2 + 5a + 6a2 + -3a2 = 0 Combine like terms: 6a2 + -3a2 = 3a2 2 + 5a + 3a2 = 0 Solving 2 + 5a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + a)(2 + 3a) = 0Subproblem 1
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Subproblem 2
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 = -0.6666666667Solution
a = {-1, -0.6666666667}
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