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Simplifying (9z + -1u)(3z + 6u) = 0 Reorder the terms: (-1u + 9z)(3z + 6u) = 0 Reorder the terms: (-1u + 9z)(6u + 3z) = 0 Multiply (-1u + 9z) * (6u + 3z) (-1u * (6u + 3z) + 9z * (6u + 3z)) = 0 ((6u * -1u + 3z * -1u) + 9z * (6u + 3z)) = 0 Reorder the terms: ((-3uz + -6u2) + 9z * (6u + 3z)) = 0 ((-3uz + -6u2) + 9z * (6u + 3z)) = 0 (-3uz + -6u2 + (6u * 9z + 3z * 9z)) = 0 (-3uz + -6u2 + (54uz + 27z2)) = 0 Reorder the terms: (-3uz + 54uz + -6u2 + 27z2) = 0 Combine like terms: -3uz + 54uz = 51uz (51uz + -6u2 + 27z2) = 0 Solving 51uz + -6u2 + 27z2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3'. 3(17uz + -2u2 + 9z2) = 0 Factor a trinomial. 3((-2u + -1z)(u + -9z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2u + -1z)' equal to zero and attempt to solve: Simplifying -2u + -1z = 0 Solving -2u + -1z = 0 Move all terms containing u to the left, all other terms to the right. Add 'z' to each side of the equation. -2u + -1z + z = 0 + z Combine like terms: -1z + z = 0 -2u + 0 = 0 + z -2u = 0 + z Remove the zero: -2u = z Divide each side by '-2'. u = -0.5z Simplifying u = -0.5zSubproblem 2
Set the factor '(u + -9z)' equal to zero and attempt to solve: Simplifying u + -9z = 0 Solving u + -9z = 0 Move all terms containing u to the left, all other terms to the right. Add '9z' to each side of the equation. u + -9z + 9z = 0 + 9z Combine like terms: -9z + 9z = 0 u + 0 = 0 + 9z u = 0 + 9z Remove the zero: u = 9z Simplifying u = 9zSolution
u = {-0.5z, 9z}
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