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Simplifying 6a2 + -23ab + 21b2 = 0 Reorder the terms: -23ab + 6a2 + 21b2 = 0 Solving -23ab + 6a2 + 21b2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -7b)(2a + -3b) = 0Subproblem 1
Set the factor '(3a + -7b)' equal to zero and attempt to solve: Simplifying 3a + -7b = 0 Solving 3a + -7b = 0 Move all terms containing a to the left, all other terms to the right. Add '7b' to each side of the equation. 3a + -7b + 7b = 0 + 7b Combine like terms: -7b + 7b = 0 3a + 0 = 0 + 7b 3a = 0 + 7b Remove the zero: 3a = 7b Divide each side by '3'. a = 2.333333333b Simplifying a = 2.333333333bSubproblem 2
Set the factor '(2a + -3b)' equal to zero and attempt to solve: Simplifying 2a + -3b = 0 Solving 2a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 2a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 2a + 0 = 0 + 3b 2a = 0 + 3b Remove the zero: 2a = 3b Divide each side by '2'. a = 1.5b Simplifying a = 1.5bSolution
a = {2.333333333b, 1.5b}
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