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Simplifying (9u + -2)(3u + 6) + (9u + -2)(8u + 5) = 0 Reorder the terms: (-2 + 9u)(3u + 6) + (9u + -2)(8u + 5) = 0 Reorder the terms: (-2 + 9u)(6 + 3u) + (9u + -2)(8u + 5) = 0 Multiply (-2 + 9u) * (6 + 3u) (-2(6 + 3u) + 9u * (6 + 3u)) + (9u + -2)(8u + 5) = 0 ((6 * -2 + 3u * -2) + 9u * (6 + 3u)) + (9u + -2)(8u + 5) = 0 ((-12 + -6u) + 9u * (6 + 3u)) + (9u + -2)(8u + 5) = 0 (-12 + -6u + (6 * 9u + 3u * 9u)) + (9u + -2)(8u + 5) = 0 (-12 + -6u + (54u + 27u2)) + (9u + -2)(8u + 5) = 0 Combine like terms: -6u + 54u = 48u (-12 + 48u + 27u2) + (9u + -2)(8u + 5) = 0 Reorder the terms: -12 + 48u + 27u2 + (-2 + 9u)(8u + 5) = 0 Reorder the terms: -12 + 48u + 27u2 + (-2 + 9u)(5 + 8u) = 0 Multiply (-2 + 9u) * (5 + 8u) -12 + 48u + 27u2 + (-2(5 + 8u) + 9u * (5 + 8u)) = 0 -12 + 48u + 27u2 + ((5 * -2 + 8u * -2) + 9u * (5 + 8u)) = 0 -12 + 48u + 27u2 + ((-10 + -16u) + 9u * (5 + 8u)) = 0 -12 + 48u + 27u2 + (-10 + -16u + (5 * 9u + 8u * 9u)) = 0 -12 + 48u + 27u2 + (-10 + -16u + (45u + 72u2)) = 0 Combine like terms: -16u + 45u = 29u -12 + 48u + 27u2 + (-10 + 29u + 72u2) = 0 Reorder the terms: -12 + -10 + 48u + 29u + 27u2 + 72u2 = 0 Combine like terms: -12 + -10 = -22 -22 + 48u + 29u + 27u2 + 72u2 = 0 Combine like terms: 48u + 29u = 77u -22 + 77u + 27u2 + 72u2 = 0 Combine like terms: 27u2 + 72u2 = 99u2 -22 + 77u + 99u2 = 0 Solving -22 + 77u + 99u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '11'. 11(-2 + 7u + 9u2) = 0 Factor a trinomial. 11((-1 + -1u)(2 + -9u)) = 0 Ignore the factor 11.Subproblem 1
Set the factor '(-1 + -1u)' equal to zero and attempt to solve: Simplifying -1 + -1u = 0 Solving -1 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1u = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1u = 0 + 1 -1u = 0 + 1 Combine like terms: 0 + 1 = 1 -1u = 1 Divide each side by '-1'. u = -1 Simplifying u = -1Subproblem 2
Set the factor '(2 + -9u)' equal to zero and attempt to solve: Simplifying 2 + -9u = 0 Solving 2 + -9u = 0 Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -9u = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9u = 0 + -2 -9u = 0 + -2 Combine like terms: 0 + -2 = -2 -9u = -2 Divide each side by '-9'. u = 0.2222222222 Simplifying u = 0.2222222222Solution
u = {-1, 0.2222222222}
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