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

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


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

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

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

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

Combine like terms: 8v + 7v = 15v
(28 + 15v + 2v2) = 0

Solving
28 + 15v + 2v2 = 0

Solving for variable 'v'.

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


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

Simplifying
4 + v = 0

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

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

Combine like terms: 0 + -4 = -4
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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