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Simplifying (8z + -1u)(5z + 4u) = 0 Reorder the terms: (-1u + 8z)(5z + 4u) = 0 Reorder the terms: (-1u + 8z)(4u + 5z) = 0 Multiply (-1u + 8z) * (4u + 5z) (-1u * (4u + 5z) + 8z * (4u + 5z)) = 0 ((4u * -1u + 5z * -1u) + 8z * (4u + 5z)) = 0 Reorder the terms: ((-5uz + -4u2) + 8z * (4u + 5z)) = 0 ((-5uz + -4u2) + 8z * (4u + 5z)) = 0 (-5uz + -4u2 + (4u * 8z + 5z * 8z)) = 0 (-5uz + -4u2 + (32uz + 40z2)) = 0 Reorder the terms: (-5uz + 32uz + -4u2 + 40z2) = 0 Combine like terms: -5uz + 32uz = 27uz (27uz + -4u2 + 40z2) = 0 Solving 27uz + -4u2 + 40z2 = 0 Solving for variable 'u'. Factor a trinomial. (-4u + -5z)(u + -8z) = 0Subproblem 1
Set the factor '(-4u + -5z)' equal to zero and attempt to solve: Simplifying -4u + -5z = 0 Solving -4u + -5z = 0 Move all terms containing u to the left, all other terms to the right. Add '5z' to each side of the equation. -4u + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 -4u + 0 = 0 + 5z -4u = 0 + 5z Remove the zero: -4u = 5z Divide each side by '-4'. u = -1.25z Simplifying u = -1.25zSubproblem 2
Set the factor '(u + -8z)' equal to zero and attempt to solve: Simplifying u + -8z = 0 Solving u + -8z = 0 Move all terms containing u to the left, all other terms to the right. Add '8z' to each side of the equation. u + -8z + 8z = 0 + 8z Combine like terms: -8z + 8z = 0 u + 0 = 0 + 8z u = 0 + 8z Remove the zero: u = 8z Simplifying u = 8zSolution
u = {-1.25z, 8z}
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