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

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 = 13u
(-14 + 13u + -3u2) = 0

Solving
-14 + 13u + -3u2 = 0

Solving for variable 'u'.

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

Subproblem 1
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
Subproblem 2
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
Solution
u = {2.333333333, 2}