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Simplifying (7z + -1u)(4z + 5u) = 0 Reorder the terms: (-1u + 7z)(4z + 5u) = 0 Reorder the terms: (-1u + 7z)(5u + 4z) = 0 Multiply (-1u + 7z) * (5u + 4z) (-1u * (5u + 4z) + 7z * (5u + 4z)) = 0 ((5u * -1u + 4z * -1u) + 7z * (5u + 4z)) = 0 Reorder the terms: ((-4uz + -5u2) + 7z * (5u + 4z)) = 0 ((-4uz + -5u2) + 7z * (5u + 4z)) = 0 (-4uz + -5u2 + (5u * 7z + 4z * 7z)) = 0 (-4uz + -5u2 + (35uz + 28z2)) = 0 Reorder the terms: (-4uz + 35uz + -5u2 + 28z2) = 0 Combine like terms: -4uz + 35uz = 31uz (31uz + -5u2 + 28z2) = 0 Solving 31uz + -5u2 + 28z2 = 0 Solving for variable 'u'. Factor a trinomial. (-5u + -4z)(u + -7z) = 0Subproblem 1
Set the factor '(-5u + -4z)' equal to zero and attempt to solve: Simplifying -5u + -4z = 0 Solving -5u + -4z = 0 Move all terms containing u to the left, all other terms to the right. Add '4z' to each side of the equation. -5u + -4z + 4z = 0 + 4z Combine like terms: -4z + 4z = 0 -5u + 0 = 0 + 4z -5u = 0 + 4z Remove the zero: -5u = 4z Divide each side by '-5'. u = -0.8z Simplifying u = -0.8zSubproblem 2
Set the factor '(u + -7z)' equal to zero and attempt to solve: Simplifying u + -7z = 0 Solving u + -7z = 0 Move all terms containing u to the left, all other terms to the right. Add '7z' to each side of the equation. u + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 u + 0 = 0 + 7z u = 0 + 7z Remove the zero: u = 7z Simplifying u = 7zSolution
u = {-0.8z, 7z}
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