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

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


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

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

Multiply (-1 + 2v) * (7 + -1v)
(-1(7 + -1v) + 2v * (7 + -1v)) = 0
((7 * -1 + -1v * -1) + 2v * (7 + -1v)) = 0
((-7 + 1v) + 2v * (7 + -1v)) = 0
(-7 + 1v + (7 * 2v + -1v * 2v)) = 0
(-7 + 1v + (14v + -2v2)) = 0

Combine like terms: 1v + 14v = 15v
(-7 + 15v + -2v2) = 0

Solving
-7 + 15v + -2v2 = 0

Solving for variable 'v'.

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


Subproblem 1
Set the factor '(-7 + v)' equal to zero and attempt to solve:

Simplifying
-7 + v = 0

Solving
-7 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + v = 0 + 7

Combine like terms: -7 + 7 = 0
0 + v = 0 + 7
v = 0 + 7

Combine like terms: 0 + 7 = 7
v = 7

Simplifying
v = 7

Subproblem 2
Set the factor '(1 + -2v)' equal to zero and attempt to solve:

Simplifying
1 + -2v = 0

Solving
1 + -2v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2v = 0 + -1

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

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

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

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

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