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Simplifying (3z + -1u)(5z + 5u) = 0 Reorder the terms: (-1u + 3z)(5z + 5u) = 0 Reorder the terms: (-1u + 3z)(5u + 5z) = 0 Multiply (-1u + 3z) * (5u + 5z) (-1u * (5u + 5z) + 3z * (5u + 5z)) = 0 ((5u * -1u + 5z * -1u) + 3z * (5u + 5z)) = 0 Reorder the terms: ((-5uz + -5u2) + 3z * (5u + 5z)) = 0 ((-5uz + -5u2) + 3z * (5u + 5z)) = 0 (-5uz + -5u2 + (5u * 3z + 5z * 3z)) = 0 (-5uz + -5u2 + (15uz + 15z2)) = 0 Reorder the terms: (-5uz + 15uz + -5u2 + 15z2) = 0 Combine like terms: -5uz + 15uz = 10uz (10uz + -5u2 + 15z2) = 0 Solving 10uz + -5u2 + 15z2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '5'. 5(2uz + -1u2 + 3z2) = 0 Factor a trinomial. 5((-1u + -1z)(u + -3z)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1u + -1z)' equal to zero and attempt to solve: Simplifying -1u + -1z = 0 Solving -1u + -1z = 0 Move all terms containing u to the left, all other terms to the right. Add 'z' to each side of the equation. -1u + -1z + z = 0 + z Combine like terms: -1z + z = 0 -1u + 0 = 0 + z -1u = 0 + z Remove the zero: -1u = z Divide each side by '-1'. u = -1z Simplifying u = -1zSubproblem 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 = {-1z, 3z}
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