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Simplifying (3b + 1a)(3b + -2a) = 0 Reorder the terms: (1a + 3b)(3b + -2a) = 0 Reorder the terms: (1a + 3b)(-2a + 3b) = 0 Multiply (1a + 3b) * (-2a + 3b) (1a * (-2a + 3b) + 3b * (-2a + 3b)) = 0 ((-2a * 1a + 3b * 1a) + 3b * (-2a + 3b)) = 0 Reorder the terms: ((3ab + -2a2) + 3b * (-2a + 3b)) = 0 ((3ab + -2a2) + 3b * (-2a + 3b)) = 0 (3ab + -2a2 + (-2a * 3b + 3b * 3b)) = 0 (3ab + -2a2 + (-6ab + 9b2)) = 0 Reorder the terms: (3ab + -6ab + -2a2 + 9b2) = 0 Combine like terms: 3ab + -6ab = -3ab (-3ab + -2a2 + 9b2) = 0 Solving -3ab + -2a2 + 9b2 = 0 Solving for variable 'a'. Factor a trinomial. (-1a + -3b)(2a + -3b) = 0Subproblem 1
Set the factor '(-1a + -3b)' equal to zero and attempt to solve: Simplifying -1a + -3b = 0 Solving -1a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. -1a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 -1a + 0 = 0 + 3b -1a = 0 + 3b Remove the zero: -1a = 3b Divide each side by '-1'. a = -3b Simplifying a = -3bSubproblem 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 = {-3b, 1.5b}
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