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Simplifying (6a + -9uv)(a + uv) = 0 Multiply (6a + -9uv) * (a + uv) (6a * (a + uv) + -9uv * (a + uv)) = 0 ((a * 6a + uv * 6a) + -9uv * (a + uv)) = 0 Reorder the terms: ((6auv + 6a2) + -9uv * (a + uv)) = 0 ((6auv + 6a2) + -9uv * (a + uv)) = 0 (6auv + 6a2 + (a * -9uv + uv * -9uv)) = 0 (6auv + 6a2 + (-9auv + -9u2v2)) = 0 Reorder the terms: (6auv + -9auv + 6a2 + -9u2v2) = 0 Combine like terms: 6auv + -9auv = -3auv (-3auv + 6a2 + -9u2v2) = 0 Solving -3auv + 6a2 + -9u2v2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1auv + 2a2 + -3u2v2) = 0 Factor a trinomial. 3((2a + -3uv)(a + uv)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2a + -3uv)' equal to zero and attempt to solve: Simplifying 2a + -3uv = 0 Solving 2a + -3uv = 0 Move all terms containing a to the left, all other terms to the right. Add '3uv' to each side of the equation. 2a + -3uv + 3uv = 0 + 3uv Combine like terms: -3uv + 3uv = 0 2a + 0 = 0 + 3uv 2a = 0 + 3uv Remove the zero: 2a = 3uv Divide each side by '2'. a = 1.5uv Simplifying a = 1.5uvSubproblem 2
Set the factor '(a + uv)' equal to zero and attempt to solve: Simplifying a + uv = 0 Solving a + uv = 0 Move all terms containing a to the left, all other terms to the right. Add '-1uv' to each side of the equation. a + uv + -1uv = 0 + -1uv Combine like terms: uv + -1uv = 0 a + 0 = 0 + -1uv a = 0 + -1uv Remove the zero: a = -1uv Simplifying a = -1uvSolution
a = {1.5uv, -1uv}
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