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Simplifying ((u + -2)(u + -2)(u + -2)) + -3u + 8 = 0 Reorder the terms: ((-2 + u)(u + -2)(u + -2)) + -3u + 8 = 0 Reorder the terms: ((-2 + u)(-2 + u)(u + -2)) + -3u + 8 = 0 Reorder the terms: ((-2 + u)(-2 + u)(-2 + u)) + -3u + 8 = 0 Multiply (-2 + u) * (-2 + u) ((-2(-2 + u) + u(-2 + u))(-2 + u)) + -3u + 8 = 0 (((-2 * -2 + u * -2) + u(-2 + u))(-2 + u)) + -3u + 8 = 0 (((4 + -2u) + u(-2 + u))(-2 + u)) + -3u + 8 = 0 ((4 + -2u + (-2 * u + u * u))(-2 + u)) + -3u + 8 = 0 ((4 + -2u + (-2u + u2))(-2 + u)) + -3u + 8 = 0 Combine like terms: -2u + -2u = -4u ((4 + -4u + u2)(-2 + u)) + -3u + 8 = 0 Multiply (4 + -4u + u2) * (-2 + u) ((4(-2 + u) + -4u * (-2 + u) + u2(-2 + u))) + -3u + 8 = 0 (((-2 * 4 + u * 4) + -4u * (-2 + u) + u2(-2 + u))) + -3u + 8 = 0 (((-8 + 4u) + -4u * (-2 + u) + u2(-2 + u))) + -3u + 8 = 0 ((-8 + 4u + (-2 * -4u + u * -4u) + u2(-2 + u))) + -3u + 8 = 0 ((-8 + 4u + (8u + -4u2) + u2(-2 + u))) + -3u + 8 = 0 ((-8 + 4u + 8u + -4u2 + (-2 * u2 + u * u2))) + -3u + 8 = 0 ((-8 + 4u + 8u + -4u2 + (-2u2 + u3))) + -3u + 8 = 0 Combine like terms: 4u + 8u = 12u ((-8 + 12u + -4u2 + -2u2 + u3)) + -3u + 8 = 0 Combine like terms: -4u2 + -2u2 = -6u2 ((-8 + 12u + -6u2 + u3)) + -3u + 8 = 0 (-8 + 12u + -6u2 + u3) + -3u + 8 = 0 Remove parenthesis around (-8 + 12u + -6u2 + u3) -8 + 12u + -6u2 + u3 + -3u + 8 = 0 Reorder the terms: -8 + 8 + 12u + -3u + -6u2 + u3 = 0 Combine like terms: -8 + 8 = 0 0 + 12u + -3u + -6u2 + u3 = 0 12u + -3u + -6u2 + u3 = 0 Combine like terms: 12u + -3u = 9u 9u + -6u2 + u3 = 0 Solving 9u + -6u2 + u3 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'u'. u(9 + -6u + u2) = 0 Factor a trinomial. u((3 + -1u)(3 + -1u)) = 0Subproblem 1
Set the factor 'u' equal to zero and attempt to solve: Simplifying u = 0 Solving u = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u = 0Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve: Simplifying 3 + -1u = 0 Solving 3 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1u = 0 + -3 -1u = 0 + -3 Combine like terms: 0 + -3 = -3 -1u = -3 Divide each side by '-1'. u = 3 Simplifying u = 3Subproblem 3
Set the factor '(3 + -1u)' equal to zero and attempt to solve: Simplifying 3 + -1u = 0 Solving 3 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1u = 0 + -3 -1u = 0 + -3 Combine like terms: 0 + -3 = -3 -1u = -3 Divide each side by '-1'. u = 3 Simplifying u = 3Solution
u = {0, 3, 3}
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