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Simplifying (4z + -1u)(4z + 3u) = 0 Reorder the terms: (-1u + 4z)(4z + 3u) = 0 Reorder the terms: (-1u + 4z)(3u + 4z) = 0 Multiply (-1u + 4z) * (3u + 4z) (-1u * (3u + 4z) + 4z * (3u + 4z)) = 0 ((3u * -1u + 4z * -1u) + 4z * (3u + 4z)) = 0 Reorder the terms: ((-4uz + -3u2) + 4z * (3u + 4z)) = 0 ((-4uz + -3u2) + 4z * (3u + 4z)) = 0 (-4uz + -3u2 + (3u * 4z + 4z * 4z)) = 0 (-4uz + -3u2 + (12uz + 16z2)) = 0 Reorder the terms: (-4uz + 12uz + -3u2 + 16z2) = 0 Combine like terms: -4uz + 12uz = 8uz (8uz + -3u2 + 16z2) = 0 Solving 8uz + -3u2 + 16z2 = 0 Solving for variable 'u'. Factor a trinomial. (-3u + -4z)(u + -4z) = 0Subproblem 1
Set the factor '(-3u + -4z)' equal to zero and attempt to solve: Simplifying -3u + -4z = 0 Solving -3u + -4z = 0 Move all terms containing u to the left, all other terms to the right. Add '4z' to each side of the equation. -3u + -4z + 4z = 0 + 4z Combine like terms: -4z + 4z = 0 -3u + 0 = 0 + 4z -3u = 0 + 4z Remove the zero: -3u = 4z Divide each side by '-3'. u = -1.333333333z Simplifying u = -1.333333333zSubproblem 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 = {-1.333333333z, 4z}
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