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Simplifying (2u + -3)(2 + u) = 0 Reorder the terms: (-3 + 2u)(2 + u) = 0 Multiply (-3 + 2u) * (2 + u) (-3(2 + u) + 2u * (2 + u)) = 0 ((2 * -3 + u * -3) + 2u * (2 + u)) = 0 ((-6 + -3u) + 2u * (2 + u)) = 0 (-6 + -3u + (2 * 2u + u * 2u)) = 0 (-6 + -3u + (4u + 2u2)) = 0 Combine like terms: -3u + 4u = 1u (-6 + 1u + 2u2) = 0 Solving -6 + 1u + 2u2 = 0 Solving for variable 'u'. Factor a trinomial. (-2 + -1u)(3 + -2u) = 0Subproblem 1
Set the factor '(-2 + -1u)' equal to zero and attempt to solve: Simplifying -2 + -1u = 0 Solving -2 + -1u = 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 + -1u = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1u = 0 + 2 -1u = 0 + 2 Combine like terms: 0 + 2 = 2 -1u = 2 Divide each side by '-1'. u = -2 Simplifying u = -2Subproblem 2
Set the factor '(3 + -2u)' equal to zero and attempt to solve: Simplifying 3 + -2u = 0 Solving 3 + -2u = 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 + -2u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2u = 0 + -3 -2u = 0 + -3 Combine like terms: 0 + -3 = -3 -2u = -3 Divide each side by '-2'. u = 1.5 Simplifying u = 1.5Solution
u = {-2, 1.5}
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