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Simplifying (8z + -1u)(7z + 5u) = 0 Reorder the terms: (-1u + 8z)(7z + 5u) = 0 Reorder the terms: (-1u + 8z)(5u + 7z) = 0 Multiply (-1u + 8z) * (5u + 7z) (-1u * (5u + 7z) + 8z * (5u + 7z)) = 0 ((5u * -1u + 7z * -1u) + 8z * (5u + 7z)) = 0 Reorder the terms: ((-7uz + -5u2) + 8z * (5u + 7z)) = 0 ((-7uz + -5u2) + 8z * (5u + 7z)) = 0 (-7uz + -5u2 + (5u * 8z + 7z * 8z)) = 0 (-7uz + -5u2 + (40uz + 56z2)) = 0 Reorder the terms: (-7uz + 40uz + -5u2 + 56z2) = 0 Combine like terms: -7uz + 40uz = 33uz (33uz + -5u2 + 56z2) = 0 Solving 33uz + -5u2 + 56z2 = 0 Solving for variable 'u'. Factor a trinomial. (-5u + -7z)(u + -8z) = 0Subproblem 1
Set the factor '(-5u + -7z)' equal to zero and attempt to solve: Simplifying -5u + -7z = 0 Solving -5u + -7z = 0 Move all terms containing u to the left, all other terms to the right. Add '7z' to each side of the equation. -5u + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 -5u + 0 = 0 + 7z -5u = 0 + 7z Remove the zero: -5u = 7z Divide each side by '-5'. u = -1.4z Simplifying u = -1.4zSubproblem 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 = {-1.4z, 8z}
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