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Simplifying (3a + -2b)(a + b) = 0 Multiply (3a + -2b) * (a + b) (3a * (a + b) + -2b * (a + b)) = 0 ((a * 3a + b * 3a) + -2b * (a + b)) = 0 Reorder the terms: ((3ab + 3a2) + -2b * (a + b)) = 0 ((3ab + 3a2) + -2b * (a + b)) = 0 (3ab + 3a2 + (a * -2b + b * -2b)) = 0 (3ab + 3a2 + (-2ab + -2b2)) = 0 Reorder the terms: (3ab + -2ab + 3a2 + -2b2) = 0 Combine like terms: 3ab + -2ab = 1ab (1ab + 3a2 + -2b2) = 0 Solving 1ab + 3a2 + -2b2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -2b)(a + b) = 0Subproblem 1
Set the factor '(3a + -2b)' equal to zero and attempt to solve: Simplifying 3a + -2b = 0 Solving 3a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 3a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 3a + 0 = 0 + 2b 3a = 0 + 2b Remove the zero: 3a = 2b Divide each side by '3'. a = 0.6666666667b Simplifying a = 0.6666666667bSubproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSolution
a = {0.6666666667b, -1b}
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