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Simplifying (3a + -4b)(a + -6b) = 0 Multiply (3a + -4b) * (a + -6b) (3a * (a + -6b) + -4b * (a + -6b)) = 0 ((a * 3a + -6b * 3a) + -4b * (a + -6b)) = 0 Reorder the terms: ((-18ab + 3a2) + -4b * (a + -6b)) = 0 ((-18ab + 3a2) + -4b * (a + -6b)) = 0 (-18ab + 3a2 + (a * -4b + -6b * -4b)) = 0 (-18ab + 3a2 + (-4ab + 24b2)) = 0 Reorder the terms: (-18ab + -4ab + 3a2 + 24b2) = 0 Combine like terms: -18ab + -4ab = -22ab (-22ab + 3a2 + 24b2) = 0 Solving -22ab + 3a2 + 24b2 = 0 Solving for variable 'a'. Factor a trinomial. (a + -6b)(3a + -4b) = 0Subproblem 1
Set the factor '(a + -6b)' equal to zero and attempt to solve: Simplifying a + -6b = 0 Solving a + -6b = 0 Move all terms containing a to the left, all other terms to the right. Add '6b' to each side of the equation. a + -6b + 6b = 0 + 6b Combine like terms: -6b + 6b = 0 a + 0 = 0 + 6b a = 0 + 6b Remove the zero: a = 6b Simplifying a = 6bSubproblem 2
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 = 1.333333333bSolution
a = {6b, 1.333333333b}
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