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Simplifying (1 + u)(3u + -7) = 0 Reorder the terms: (1 + u)(-7 + 3u) = 0 Multiply (1 + u) * (-7 + 3u) (1(-7 + 3u) + u(-7 + 3u)) = 0 ((-7 * 1 + 3u * 1) + u(-7 + 3u)) = 0 ((-7 + 3u) + u(-7 + 3u)) = 0 (-7 + 3u + (-7 * u + 3u * u)) = 0 (-7 + 3u + (-7u + 3u2)) = 0 Combine like terms: 3u + -7u = -4u (-7 + -4u + 3u2) = 0 Solving -7 + -4u + 3u2 = 0 Solving for variable 'u'. Factor a trinomial. (-1 + -1u)(7 + -3u) = 0Subproblem 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 '(7 + -3u)' equal to zero and attempt to solve: Simplifying 7 + -3u = 0 Solving 7 + -3u = 0 Move all terms containing u to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3u = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3u = 0 + -7 -3u = 0 + -7 Combine like terms: 0 + -7 = -7 -3u = -7 Divide each side by '-3'. u = 2.333333333 Simplifying u = 2.333333333Solution
u = {-1, 2.333333333}
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