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Simplifying (3a + 2b)(6a + -1b) = 0 Multiply (3a + 2b) * (6a + -1b) (3a * (6a + -1b) + 2b * (6a + -1b)) = 0 ((6a * 3a + -1b * 3a) + 2b * (6a + -1b)) = 0 Reorder the terms: ((-3ab + 18a2) + 2b * (6a + -1b)) = 0 ((-3ab + 18a2) + 2b * (6a + -1b)) = 0 (-3ab + 18a2 + (6a * 2b + -1b * 2b)) = 0 (-3ab + 18a2 + (12ab + -2b2)) = 0 Reorder the terms: (-3ab + 12ab + 18a2 + -2b2) = 0 Combine like terms: -3ab + 12ab = 9ab (9ab + 18a2 + -2b2) = 0 Solving 9ab + 18a2 + -2b2 = 0 Solving for variable 'a'. Factor a trinomial. (6a + -1b)(3a + 2b) = 0Subproblem 1
Set the factor '(6a + -1b)' equal to zero and attempt to solve: Simplifying 6a + -1b = 0 Solving 6a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 6a + -1b + b = 0 + b Combine like terms: -1b + b = 0 6a + 0 = 0 + b 6a = 0 + b Remove the zero: 6a = b Divide each side by '6'. a = 0.1666666667b Simplifying a = 0.1666666667bSubproblem 2
Set the factor '(3a + 2b)' equal to zero and attempt to solve: Simplifying 3a + 2b = 0 Solving 3a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 3a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 3a + 0 = 0 + -2b 3a = 0 + -2b Remove the zero: 3a = -2b Divide each side by '3'. a = -0.6666666667b Simplifying a = -0.6666666667bSolution
a = {0.1666666667b, -0.6666666667b}
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