(2u-1)(7-u)=0

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Solution for (2u-1)(7-u)=0 equation: 


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

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

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

Combine like terms: 1u + 14u = 15u
(-7 + 15u + -2u2) = 0

Solving
-7 + 15u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + u)(1 + -2u) = 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 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 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 + -2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2u = 0 + -1
-2u = 0 + -1

Combine like terms: 0 + -1 = -1
-2u = -1

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {7, 0.5}

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