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Simplifying (a + 2b)(3a + -4b) = 0 Multiply (a + 2b) * (3a + -4b) (a(3a + -4b) + 2b * (3a + -4b)) = 0 ((3a * a + -4b * a) + 2b * (3a + -4b)) = 0 Reorder the terms: ((-4ab + 3a2) + 2b * (3a + -4b)) = 0 ((-4ab + 3a2) + 2b * (3a + -4b)) = 0 (-4ab + 3a2 + (3a * 2b + -4b * 2b)) = 0 (-4ab + 3a2 + (6ab + -8b2)) = 0 Reorder the terms: (-4ab + 6ab + 3a2 + -8b2) = 0 Combine like terms: -4ab + 6ab = 2ab (2ab + 3a2 + -8b2) = 0 Solving 2ab + 3a2 + -8b2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -4b)(a + 2b) = 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 + 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 = {1.333333333b, -2b}
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