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Simplifying (-2a + 3b)(-1b + 6a) = 0 Reorder the terms: (-2a + 3b)(6a + -1b) = 0 Multiply (-2a + 3b) * (6a + -1b) (-2a * (6a + -1b) + 3b * (6a + -1b)) = 0 ((6a * -2a + -1b * -2a) + 3b * (6a + -1b)) = 0 Reorder the terms: ((2ab + -12a2) + 3b * (6a + -1b)) = 0 ((2ab + -12a2) + 3b * (6a + -1b)) = 0 (2ab + -12a2 + (6a * 3b + -1b * 3b)) = 0 (2ab + -12a2 + (18ab + -3b2)) = 0 Reorder the terms: (2ab + 18ab + -12a2 + -3b2) = 0 Combine like terms: 2ab + 18ab = 20ab (20ab + -12a2 + -3b2) = 0 Solving 20ab + -12a2 + -3b2 = 0 Solving for variable 'a'. Factor a trinomial. (-6a + b)(2a + -3b) = 0Subproblem 1
Set the factor '(-6a + b)' equal to zero and attempt to solve: Simplifying -6a + b = 0 Solving -6a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. -6a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 -6a + 0 = 0 + -1b -6a = 0 + -1b Remove the zero: -6a = -1b Divide each side by '-6'. a = 0.1666666667b Simplifying a = 0.1666666667bSubproblem 2
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 = 1.5bSolution
a = {0.1666666667b, 1.5b}
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