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Simplifying (9z + -1u)(5z + 6u) = 0 Reorder the terms: (-1u + 9z)(5z + 6u) = 0 Reorder the terms: (-1u + 9z)(6u + 5z) = 0 Multiply (-1u + 9z) * (6u + 5z) (-1u * (6u + 5z) + 9z * (6u + 5z)) = 0 ((6u * -1u + 5z * -1u) + 9z * (6u + 5z)) = 0 Reorder the terms: ((-5uz + -6u2) + 9z * (6u + 5z)) = 0 ((-5uz + -6u2) + 9z * (6u + 5z)) = 0 (-5uz + -6u2 + (6u * 9z + 5z * 9z)) = 0 (-5uz + -6u2 + (54uz + 45z2)) = 0 Reorder the terms: (-5uz + 54uz + -6u2 + 45z2) = 0 Combine like terms: -5uz + 54uz = 49uz (49uz + -6u2 + 45z2) = 0 Solving 49uz + -6u2 + 45z2 = 0 Solving for variable 'u'. Factor a trinomial. (-6u + -5z)(u + -9z) = 0Subproblem 1
Set the factor '(-6u + -5z)' equal to zero and attempt to solve: Simplifying -6u + -5z = 0 Solving -6u + -5z = 0 Move all terms containing u to the left, all other terms to the right. Add '5z' to each side of the equation. -6u + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 -6u + 0 = 0 + 5z -6u = 0 + 5z Remove the zero: -6u = 5z Divide each side by '-6'. u = -0.8333333333z Simplifying u = -0.8333333333zSubproblem 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 = {-0.8333333333z, 9z}
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