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Simplifying (3a + -1b)(2a + b) = 0 Multiply (3a + -1b) * (2a + b) (3a * (2a + b) + -1b * (2a + b)) = 0 ((2a * 3a + b * 3a) + -1b * (2a + b)) = 0 Reorder the terms: ((3ab + 6a2) + -1b * (2a + b)) = 0 ((3ab + 6a2) + -1b * (2a + b)) = 0 (3ab + 6a2 + (2a * -1b + b * -1b)) = 0 (3ab + 6a2 + (-2ab + -1b2)) = 0 Reorder the terms: (3ab + -2ab + 6a2 + -1b2) = 0 Combine like terms: 3ab + -2ab = 1ab (1ab + 6a2 + -1b2) = 0 Solving 1ab + 6a2 + -1b2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -1b)(2a + b) = 0Subproblem 1
Set the factor '(3a + -1b)' equal to zero and attempt to solve: Simplifying 3a + -1b = 0 Solving 3a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 3a + -1b + b = 0 + b Combine like terms: -1b + b = 0 3a + 0 = 0 + b 3a = 0 + b Remove the zero: 3a = b Divide each side by '3'. a = 0.3333333333b Simplifying a = 0.3333333333bSubproblem 2
Set the factor '(2a + b)' equal to zero and attempt to solve: Simplifying 2a + b = 0 Solving 2a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 2a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 2a + 0 = 0 + -1b 2a = 0 + -1b Remove the zero: 2a = -1b Divide each side by '2'. a = -0.5b Simplifying a = -0.5bSolution
a = {0.3333333333b, -0.5b}
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