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Simplifying (4z + -1u)(3z + 5u) = 0 Reorder the terms: (-1u + 4z)(3z + 5u) = 0 Reorder the terms: (-1u + 4z)(5u + 3z) = 0 Multiply (-1u + 4z) * (5u + 3z) (-1u * (5u + 3z) + 4z * (5u + 3z)) = 0 ((5u * -1u + 3z * -1u) + 4z * (5u + 3z)) = 0 Reorder the terms: ((-3uz + -5u2) + 4z * (5u + 3z)) = 0 ((-3uz + -5u2) + 4z * (5u + 3z)) = 0 (-3uz + -5u2 + (5u * 4z + 3z * 4z)) = 0 (-3uz + -5u2 + (20uz + 12z2)) = 0 Reorder the terms: (-3uz + 20uz + -5u2 + 12z2) = 0 Combine like terms: -3uz + 20uz = 17uz (17uz + -5u2 + 12z2) = 0 Solving 17uz + -5u2 + 12z2 = 0 Solving for variable 'u'. Factor a trinomial. (-5u + -3z)(u + -4z) = 0Subproblem 1
Set the factor '(-5u + -3z)' equal to zero and attempt to solve: Simplifying -5u + -3z = 0 Solving -5u + -3z = 0 Move all terms containing u to the left, all other terms to the right. Add '3z' to each side of the equation. -5u + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 -5u + 0 = 0 + 3z -5u = 0 + 3z Remove the zero: -5u = 3z Divide each side by '-5'. u = -0.6z Simplifying u = -0.6zSubproblem 2
Set the factor '(u + -4z)' equal to zero and attempt to solve: Simplifying u + -4z = 0 Solving u + -4z = 0 Move all terms containing u to the left, all other terms to the right. Add '4z' to each side of the equation. u + -4z + 4z = 0 + 4z Combine like terms: -4z + 4z = 0 u + 0 = 0 + 4z u = 0 + 4z Remove the zero: u = 4z Simplifying u = 4zSolution
u = {-0.6z, 4z}
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