(v+7)(3v+8)=0

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Solution for (v+7)(3v+8)=0 equation: 


Simplifying
(v + 7)(3v + 8) = 0

Reorder the terms:
(7 + v)(3v + 8) = 0

Reorder the terms:
(7 + v)(8 + 3v) = 0

Multiply (7 + v) * (8 + 3v)
(7(8 + 3v) + v(8 + 3v)) = 0
((8 * 7 + 3v * 7) + v(8 + 3v)) = 0
((56 + 21v) + v(8 + 3v)) = 0
(56 + 21v + (8 * v + 3v * v)) = 0
(56 + 21v + (8v + 3v2)) = 0

Combine like terms: 21v + 8v = 29v
(56 + 29v + 3v2) = 0

Solving
56 + 29v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(7 + v)(8 + 3v) = 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 '(8 + 3v)' equal to zero and attempt to solve:

Simplifying
8 + 3v = 0

Solving
8 + 3v = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3v = 0 + -8
3v = 0 + -8

Combine like terms: 0 + -8 = -8
3v = -8

Divide each side by '3'.
v = -2.666666667

Simplifying
v = -2.666666667
Solution
v = {-7, -2.666666667}

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