(4v+2)(3+v)=0

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Solution for (4v+2)(3+v)=0 equation:


Simplifying
(4v + 2)(3 + v) = 0

Reorder the terms:
(2 + 4v)(3 + v) = 0

Multiply (2 + 4v) * (3 + v)
(2(3 + v) + 4v * (3 + v)) = 0
((3 * 2 + v * 2) + 4v * (3 + v)) = 0
((6 + 2v) + 4v * (3 + v)) = 0
(6 + 2v + (3 * 4v + v * 4v)) = 0
(6 + 2v + (12v + 4v2)) = 0

Combine like terms: 2v + 12v = 14v
(6 + 14v + 4v2) = 0

Solving
6 + 14v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 7v + 2v2) = 0

Factor a trinomial.
2((3 + v)(1 + 2v)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3

Subproblem 2

Set the factor '(1 + 2v)' equal to zero and attempt to solve: Simplifying 1 + 2v = 0 Solving 1 + 2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2v = 0 + -1 2v = 0 + -1 Combine like terms: 0 + -1 = -1 2v = -1 Divide each side by '2'. v = -0.5 Simplifying v = -0.5

Solution

v = {-3, -0.5}

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