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

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Solution for (5+v)(2v-7)=0 equation: 


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

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

Multiply (5 + v) * (-7 + 2v)
(5(-7 + 2v) + v(-7 + 2v)) = 0
((-7 * 5 + 2v * 5) + v(-7 + 2v)) = 0
((-35 + 10v) + v(-7 + 2v)) = 0
(-35 + 10v + (-7 * v + 2v * v)) = 0
(-35 + 10v + (-7v + 2v2)) = 0

Combine like terms: 10v + -7v = 3v
(-35 + 3v + 2v2) = 0

Solving
-35 + 3v + 2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-5 + -1v)(7 + -2v) = 0


Subproblem 1
Set the factor '(-5 + -1v)' equal to zero and attempt to solve:

Simplifying
-5 + -1v = 0

Solving
-5 + -1v = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1v = 0 + 5
-1v = 0 + 5

Combine like terms: 0 + 5 = 5
-1v = 5

Divide each side by '-1'.
v = -5

Simplifying
v = -5

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 = {-5, 3.5}

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