(3u+7)(2-u)=0

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Solution for (3u+7)(2-u)=0 equation: 


Simplifying
(3u + 7)(2 + -1u) = 0

Reorder the terms:
(7 + 3u)(2 + -1u) = 0

Multiply (7 + 3u) * (2 + -1u)
(7(2 + -1u) + 3u * (2 + -1u)) = 0
((2 * 7 + -1u * 7) + 3u * (2 + -1u)) = 0
((14 + -7u) + 3u * (2 + -1u)) = 0
(14 + -7u + (2 * 3u + -1u * 3u)) = 0
(14 + -7u + (6u + -3u2)) = 0

Combine like terms: -7u + 6u = -1u
(14 + -1u + -3u2) = 0

Solving
14 + -1u + -3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(2 + -1u)(7 + 3u) = 0


Subproblem 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 = 2

Subproblem 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 = -2.333333333
Solution
u = {2, -2.333333333}

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