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

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


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

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

Multiply (2 + v) * (-7 + 4v)
(2(-7 + 4v) + v(-7 + 4v)) = 0
((-7 * 2 + 4v * 2) + v(-7 + 4v)) = 0
((-14 + 8v) + v(-7 + 4v)) = 0
(-14 + 8v + (-7 * v + 4v * v)) = 0
(-14 + 8v + (-7v + 4v2)) = 0

Combine like terms: 8v + -7v = 1v
(-14 + 1v + 4v2) = 0

Solving
-14 + 1v + 4v2 = 0

Solving for variable 'v'.

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


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

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

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

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

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

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

Divide each side by '-1'.
v = -2

Simplifying
v = -2

Subproblem 2
Set the factor '(7 + -4v)' equal to zero and attempt to solve:

Simplifying
7 + -4v = 0

Solving
7 + -4v = 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 + -4v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4v = 0 + -7
-4v = 0 + -7

Combine like terms: 0 + -7 = -7
-4v = -7

Divide each side by '-4'.
v = 1.75

Simplifying
v = 1.75
Solution
v = {-2, 1.75}

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