(2v+1)(2v+3)=0

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Solution for (2v+1)(2v+3)=0 equation:


Simplifying
(2v + 1)(2v + 3) = 0

Reorder the terms:
(1 + 2v)(2v + 3) = 0

Reorder the terms:
(1 + 2v)(3 + 2v) = 0

Multiply (1 + 2v) * (3 + 2v)
(1(3 + 2v) + 2v * (3 + 2v)) = 0
((3 * 1 + 2v * 1) + 2v * (3 + 2v)) = 0
((3 + 2v) + 2v * (3 + 2v)) = 0
(3 + 2v + (3 * 2v + 2v * 2v)) = 0
(3 + 2v + (6v + 4v2)) = 0

Combine like terms: 2v + 6v = 8v
(3 + 8v + 4v2) = 0

Solving
3 + 8v + 4v2 = 0

Solving for variable 'v'.

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

Subproblem 1

Set the factor '(3 + 2v)' equal to zero and attempt to solve: Simplifying 3 + 2v = 0 Solving 3 + 2v = 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 + 2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2v = 0 + -3 2v = 0 + -3 Combine like terms: 0 + -3 = -3 2v = -3 Divide each side by '2'. v = -1.5 Simplifying v = -1.5

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 = {-1.5, -0.5}

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