(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 = 20u
(7 + 20u + -3u2) = 0

Solving
7 + 20u + -3u2 = 0

Solving for variable 'u'.

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

Subproblem 1

Set the factor '(7 + -1u)' equal to zero and attempt to solve: Simplifying 7 + -1u = 0 Solving 7 + -1u = 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 + -1u = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1u = 0 + -7 -1u = 0 + -7 Combine like terms: 0 + -7 = -7 -1u = -7 Divide each side by '-1'. 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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