(3u-1)(7-u)=0

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Solution for (3u-1)(7-u)=0 equation:


Simplifying
(3u + -1)(7 + -1u) = 0

Reorder the terms:
(-1 + 3u)(7 + -1u) = 0

Multiply (-1 + 3u) * (7 + -1u)
(-1(7 + -1u) + 3u * (7 + -1u)) = 0
((7 * -1 + -1u * -1) + 3u * (7 + -1u)) = 0
((-7 + 1u) + 3u * (7 + -1u)) = 0
(-7 + 1u + (7 * 3u + -1u * 3u)) = 0
(-7 + 1u + (21u + -3u2)) = 0

Combine like terms: 1u + 21u = 22u
(-7 + 22u + -3u2) = 0

Solving
-7 + 22u + -3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + u)(1 + -3u) = 0

Subproblem 1

Set the factor '(-7 + u)' equal to zero and attempt to solve: Simplifying -7 + u = 0 Solving -7 + u = 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 + u = 0 + 7 Combine like terms: -7 + 7 = 0 0 + u = 0 + 7 u = 0 + 7 Combine like terms: 0 + 7 = 7 u = 7 Simplifying u = 7

Subproblem 2

Set the factor '(1 + -3u)' equal to zero and attempt to solve: Simplifying 1 + -3u = 0 Solving 1 + -3u = 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 + -3u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3u = 0 + -1 -3u = 0 + -1 Combine like terms: 0 + -1 = -1 -3u = -1 Divide each side by '-3'. u = 0.3333333333 Simplifying u = 0.3333333333

Solution

u = {7, 0.3333333333}

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