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Simplifying 3a2 + 5ab + -12b2 = 0 Reorder the terms: 5ab + 3a2 + -12b2 = 0 Solving 5ab + 3a2 + -12b2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -4b)(a + 3b) = 0Subproblem 1
Set the factor '(3a + -4b)' equal to zero and attempt to solve: Simplifying 3a + -4b = 0 Solving 3a + -4b = 0 Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 3a + -4b + 4b = 0 + 4b Combine like terms: -4b + 4b = 0 3a + 0 = 0 + 4b 3a = 0 + 4b Remove the zero: 3a = 4b Divide each side by '3'. a = 1.333333333b Simplifying a = 1.333333333bSubproblem 2
Set the factor '(a + 3b)' equal to zero and attempt to solve: Simplifying a + 3b = 0 Solving a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 a + 0 = 0 + -3b a = 0 + -3b Remove the zero: a = -3b Simplifying a = -3bSolution
a = {1.333333333b, -3b}
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