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Simplifying 4a2 + 8ab + 3ab + 6b2 = 0 Reorder the terms: 8ab + 3ab + 4a2 + 6b2 = 0 Combine like terms: 8ab + 3ab = 11ab 11ab + 4a2 + 6b2 = 0 Solving 11ab + 4a2 + 6b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + 3b)(a + 2b) = 0Subproblem 1
Set the factor '(4a + 3b)' equal to zero and attempt to solve: Simplifying 4a + 3b = 0 Solving 4a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 4a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 4a + 0 = 0 + -3b 4a = 0 + -3b Remove the zero: 4a = -3b Divide each side by '4'. a = -0.75b Simplifying a = -0.75bSubproblem 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 = {-0.75b, -2b}
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