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Simplifying 3a2 + 5ab + -2b2 = 0 Reorder the terms: 5ab + 3a2 + -2b2 = 0 Solving 5ab + 3a2 + -2b2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -1b)(a + 2b) = 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 '(a + 2b)' equal to zero and attempt to solve: Simplifying a + 2b = 0 Solving a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 a + 0 = 0 + -2b a = 0 + -2b Remove the zero: a = -2b Simplifying a = -2bSolution
a = {0.3333333333b, -2b}
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