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