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Simplifying (3u + -9)(4u + 7) + (3u + -9)(2u + 8) = 0 Reorder the terms: (-9 + 3u)(4u + 7) + (3u + -9)(2u + 8) = 0 Reorder the terms: (-9 + 3u)(7 + 4u) + (3u + -9)(2u + 8) = 0 Multiply (-9 + 3u) * (7 + 4u) (-9(7 + 4u) + 3u * (7 + 4u)) + (3u + -9)(2u + 8) = 0 ((7 * -9 + 4u * -9) + 3u * (7 + 4u)) + (3u + -9)(2u + 8) = 0 ((-63 + -36u) + 3u * (7 + 4u)) + (3u + -9)(2u + 8) = 0 (-63 + -36u + (7 * 3u + 4u * 3u)) + (3u + -9)(2u + 8) = 0 (-63 + -36u + (21u + 12u2)) + (3u + -9)(2u + 8) = 0 Combine like terms: -36u + 21u = -15u (-63 + -15u + 12u2) + (3u + -9)(2u + 8) = 0 Reorder the terms: -63 + -15u + 12u2 + (-9 + 3u)(2u + 8) = 0 Reorder the terms: -63 + -15u + 12u2 + (-9 + 3u)(8 + 2u) = 0 Multiply (-9 + 3u) * (8 + 2u) -63 + -15u + 12u2 + (-9(8 + 2u) + 3u * (8 + 2u)) = 0 -63 + -15u + 12u2 + ((8 * -9 + 2u * -9) + 3u * (8 + 2u)) = 0 -63 + -15u + 12u2 + ((-72 + -18u) + 3u * (8 + 2u)) = 0 -63 + -15u + 12u2 + (-72 + -18u + (8 * 3u + 2u * 3u)) = 0 -63 + -15u + 12u2 + (-72 + -18u + (24u + 6u2)) = 0 Combine like terms: -18u + 24u = 6u -63 + -15u + 12u2 + (-72 + 6u + 6u2) = 0 Reorder the terms: -63 + -72 + -15u + 6u + 12u2 + 6u2 = 0 Combine like terms: -63 + -72 = -135 -135 + -15u + 6u + 12u2 + 6u2 = 0 Combine like terms: -15u + 6u = -9u -135 + -9u + 12u2 + 6u2 = 0 Combine like terms: 12u2 + 6u2 = 18u2 -135 + -9u + 18u2 = 0 Solving -135 + -9u + 18u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '9'. 9(-15 + -1u + 2u2) = 0 Factor a trinomial. 9((-5 + -2u)(3 + -1u)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-5 + -2u)' equal to zero and attempt to solve: Simplifying -5 + -2u = 0 Solving -5 + -2u = 0 Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2u = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2u = 0 + 5 -2u = 0 + 5 Combine like terms: 0 + 5 = 5 -2u = 5 Divide each side by '-2'. u = -2.5 Simplifying u = -2.5Subproblem 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 = 3Solution
u = {-2.5, 3}
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