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Simplifying (4a + 6b)(a + -1b) = 0 Multiply (4a + 6b) * (a + -1b) (4a * (a + -1b) + 6b * (a + -1b)) = 0 ((a * 4a + -1b * 4a) + 6b * (a + -1b)) = 0 Reorder the terms: ((-4ab + 4a2) + 6b * (a + -1b)) = 0 ((-4ab + 4a2) + 6b * (a + -1b)) = 0 (-4ab + 4a2 + (a * 6b + -1b * 6b)) = 0 (-4ab + 4a2 + (6ab + -6b2)) = 0 Reorder the terms: (-4ab + 6ab + 4a2 + -6b2) = 0 Combine like terms: -4ab + 6ab = 2ab (2ab + 4a2 + -6b2) = 0 Solving 2ab + 4a2 + -6b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(ab + 2a2 + -3b2) = 0 Factor a trinomial. 2((a + -1b)(2a + 3b)) = 0 Ignore the factor 2.Subproblem 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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