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Simplifying (2a + b)(b + -3a) = 0 Reorder the terms: (2a + b)(-3a + b) = 0 Multiply (2a + b) * (-3a + b) (2a * (-3a + b) + b(-3a + b)) = 0 ((-3a * 2a + b * 2a) + b(-3a + b)) = 0 Reorder the terms: ((2ab + -6a2) + b(-3a + b)) = 0 ((2ab + -6a2) + b(-3a + b)) = 0 (2ab + -6a2 + (-3a * b + b * b)) = 0 (2ab + -6a2 + (-3ab + b2)) = 0 Reorder the terms: (2ab + -3ab + -6a2 + b2) = 0 Combine like terms: 2ab + -3ab = -1ab (-1ab + -6a2 + b2) = 0 Solving -1ab + -6a2 + b2 = 0 Solving for variable 'a'. Factor a trinomial. (-2a + -1b)(3a + -1b) = 0Subproblem 1
Set the factor '(-2a + -1b)' equal to zero and attempt to solve: Simplifying -2a + -1b = 0 Solving -2a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. -2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 -2a + 0 = 0 + b -2a = 0 + b Remove the zero: -2a = b Divide each side by '-2'. a = -0.5b Simplifying a = -0.5bSubproblem 2
Set the factor '(3a + -1b)' equal to zero and attempt to solve: Simplifying 3a + -1b = 0 Solving 3a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 3a + -1b + b = 0 + b Combine like terms: -1b + b = 0 3a + 0 = 0 + b 3a = 0 + b Remove the zero: 3a = b Divide each side by '3'. a = 0.3333333333b Simplifying a = 0.3333333333bSolution
a = {-0.5b, 0.3333333333b}
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