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Simplifying (3z + -1u)(5z + 2u) = 0 Reorder the terms: (-1u + 3z)(5z + 2u) = 0 Reorder the terms: (-1u + 3z)(2u + 5z) = 0 Multiply (-1u + 3z) * (2u + 5z) (-1u * (2u + 5z) + 3z * (2u + 5z)) = 0 ((2u * -1u + 5z * -1u) + 3z * (2u + 5z)) = 0 Reorder the terms: ((-5uz + -2u2) + 3z * (2u + 5z)) = 0 ((-5uz + -2u2) + 3z * (2u + 5z)) = 0 (-5uz + -2u2 + (2u * 3z + 5z * 3z)) = 0 (-5uz + -2u2 + (6uz + 15z2)) = 0 Reorder the terms: (-5uz + 6uz + -2u2 + 15z2) = 0 Combine like terms: -5uz + 6uz = 1uz (1uz + -2u2 + 15z2) = 0 Solving 1uz + -2u2 + 15z2 = 0 Solving for variable 'u'. Factor a trinomial. (-2u + -5z)(u + -3z) = 0Subproblem 1
Set the factor '(-2u + -5z)' equal to zero and attempt to solve: Simplifying -2u + -5z = 0 Solving -2u + -5z = 0 Move all terms containing u to the left, all other terms to the right. Add '5z' to each side of the equation. -2u + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 -2u + 0 = 0 + 5z -2u = 0 + 5z Remove the zero: -2u = 5z Divide each side by '-2'. u = -2.5z Simplifying u = -2.5zSubproblem 2
Set the factor '(u + -3z)' equal to zero and attempt to solve: Simplifying u + -3z = 0 Solving u + -3z = 0 Move all terms containing u to the left, all other terms to the right. Add '3z' to each side of the equation. u + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 u + 0 = 0 + 3z u = 0 + 3z Remove the zero: u = 3z Simplifying u = 3zSolution
u = {-2.5z, 3z}
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