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Simplifying (4z + -1u)(2z + 2u) = 0 Reorder the terms: (-1u + 4z)(2z + 2u) = 0 Reorder the terms: (-1u + 4z)(2u + 2z) = 0 Multiply (-1u + 4z) * (2u + 2z) (-1u * (2u + 2z) + 4z * (2u + 2z)) = 0 ((2u * -1u + 2z * -1u) + 4z * (2u + 2z)) = 0 Reorder the terms: ((-2uz + -2u2) + 4z * (2u + 2z)) = 0 ((-2uz + -2u2) + 4z * (2u + 2z)) = 0 (-2uz + -2u2 + (2u * 4z + 2z * 4z)) = 0 (-2uz + -2u2 + (8uz + 8z2)) = 0 Reorder the terms: (-2uz + 8uz + -2u2 + 8z2) = 0 Combine like terms: -2uz + 8uz = 6uz (6uz + -2u2 + 8z2) = 0 Solving 6uz + -2u2 + 8z2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(3uz + -1u2 + 4z2) = 0 Factor a trinomial. 2((-1u + -1z)(u + -4z)) = 0 Ignore the factor 2.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 + -4z)' equal to zero and attempt to solve: Simplifying u + -4z = 0 Solving u + -4z = 0 Move all terms containing u to the left, all other terms to the right. Add '4z' to each side of the equation. u + -4z + 4z = 0 + 4z Combine like terms: -4z + 4z = 0 u + 0 = 0 + 4z u = 0 + 4z Remove the zero: u = 4z Simplifying u = 4zSolution
u = {-1z, 4z}
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