(2v+7)(4-v)=0

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Solution for (2v+7)(4-v)=0 equation: 


Simplifying
(2v + 7)(4 + -1v) = 0

Reorder the terms:
(7 + 2v)(4 + -1v) = 0

Multiply (7 + 2v) * (4 + -1v)
(7(4 + -1v) + 2v * (4 + -1v)) = 0
((4 * 7 + -1v * 7) + 2v * (4 + -1v)) = 0
((28 + -7v) + 2v * (4 + -1v)) = 0
(28 + -7v + (4 * 2v + -1v * 2v)) = 0
(28 + -7v + (8v + -2v2)) = 0

Combine like terms: -7v + 8v = 1v
(28 + 1v + -2v2) = 0

Solving
28 + 1v + -2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(4 + -1v)(7 + 2v) = 0


Subproblem 1
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4

Subproblem 2
Set the factor '(7 + 2v)' equal to zero and attempt to solve:

Simplifying
7 + 2v = 0

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

Combine like terms: 7 + -7 = 0
0 + 2v = 0 + -7
2v = 0 + -7

Combine like terms: 0 + -7 = -7
2v = -7

Divide each side by '2'.
v = -3.5

Simplifying
v = -3.5
Solution
v = {4, -3.5}

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