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Simplifying (3z + -1u)(7z + 4u) = 0 Reorder the terms: (-1u + 3z)(7z + 4u) = 0 Reorder the terms: (-1u + 3z)(4u + 7z) = 0 Multiply (-1u + 3z) * (4u + 7z) (-1u * (4u + 7z) + 3z * (4u + 7z)) = 0 ((4u * -1u + 7z * -1u) + 3z * (4u + 7z)) = 0 Reorder the terms: ((-7uz + -4u2) + 3z * (4u + 7z)) = 0 ((-7uz + -4u2) + 3z * (4u + 7z)) = 0 (-7uz + -4u2 + (4u * 3z + 7z * 3z)) = 0 (-7uz + -4u2 + (12uz + 21z2)) = 0 Reorder the terms: (-7uz + 12uz + -4u2 + 21z2) = 0 Combine like terms: -7uz + 12uz = 5uz (5uz + -4u2 + 21z2) = 0 Solving 5uz + -4u2 + 21z2 = 0 Solving for variable 'u'. Factor a trinomial. (-4u + -7z)(u + -3z) = 0Subproblem 1
Set the factor '(-4u + -7z)' equal to zero and attempt to solve: Simplifying -4u + -7z = 0 Solving -4u + -7z = 0 Move all terms containing u to the left, all other terms to the right. Add '7z' to each side of the equation. -4u + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 -4u + 0 = 0 + 7z -4u = 0 + 7z Remove the zero: -4u = 7z Divide each side by '-4'. u = -1.75z Simplifying u = -1.75zSubproblem 2
Set the factor '(u + -3z)' equal to zero and attempt to solve: Simplifying u + -3z = 0 Solving u + -3z = 0 Move all terms containing u to the left, all other terms to the right. Add '3z' to each side of the equation. u + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 u + 0 = 0 + 3z u = 0 + 3z Remove the zero: u = 3z Simplifying u = 3zSolution
u = {-1.75z, 3z}
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