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Simplifying (3u + -2)(2u + 1) + -5u(u + 3) = 103 Reorder the terms: (-2 + 3u)(2u + 1) + -5u(u + 3) = 103 Reorder the terms: (-2 + 3u)(1 + 2u) + -5u(u + 3) = 103 Multiply (-2 + 3u) * (1 + 2u) (-2(1 + 2u) + 3u * (1 + 2u)) + -5u(u + 3) = 103 ((1 * -2 + 2u * -2) + 3u * (1 + 2u)) + -5u(u + 3) = 103 ((-2 + -4u) + 3u * (1 + 2u)) + -5u(u + 3) = 103 (-2 + -4u + (1 * 3u + 2u * 3u)) + -5u(u + 3) = 103 (-2 + -4u + (3u + 6u2)) + -5u(u + 3) = 103 Combine like terms: -4u + 3u = -1u (-2 + -1u + 6u2) + -5u(u + 3) = 103 Reorder the terms: -2 + -1u + 6u2 + -5u(3 + u) = 103 -2 + -1u + 6u2 + (3 * -5u + u * -5u) = 103 -2 + -1u + 6u2 + (-15u + -5u2) = 103 Reorder the terms: -2 + -1u + -15u + 6u2 + -5u2 = 103 Combine like terms: -1u + -15u = -16u -2 + -16u + 6u2 + -5u2 = 103 Combine like terms: 6u2 + -5u2 = 1u2 -2 + -16u + 1u2 = 103 Solving -2 + -16u + 1u2 = 103 Solving for variable 'u'. Reorder the terms: -2 + -103 + -16u + 1u2 = 103 + -103 Combine like terms: -2 + -103 = -105 -105 + -16u + 1u2 = 103 + -103 Combine like terms: 103 + -103 = 0 -105 + -16u + 1u2 = 0 Factor a trinomial. (-5 + -1u)(21 + -1u) = 0Subproblem 1
Set the factor '(-5 + -1u)' equal to zero and attempt to solve: Simplifying -5 + -1u = 0 Solving -5 + -1u = 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 + -1u = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1u = 0 + 5 -1u = 0 + 5 Combine like terms: 0 + 5 = 5 -1u = 5 Divide each side by '-1'. u = -5 Simplifying u = -5Subproblem 2
Set the factor '(21 + -1u)' equal to zero and attempt to solve: Simplifying 21 + -1u = 0 Solving 21 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1u = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1u = 0 + -21 -1u = 0 + -21 Combine like terms: 0 + -21 = -21 -1u = -21 Divide each side by '-1'. u = 21 Simplifying u = 21Solution
u = {-5, 21}
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