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Simplifying 4a2 + 14ab + 12b2 = 0 Reorder the terms: 14ab + 4a2 + 12b2 = 0 Solving 14ab + 4a2 + 12b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(7ab + 2a2 + 6b2) = 0 Factor a trinomial. 2((2a + 3b)(a + 2b)) = 0 Ignore the factor 2.Subproblem 1
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 = -1.5bSubproblem 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 = {-1.5b, -2b}
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