(4v+1)(6+v)=0

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Solution for (4v+1)(6+v)=0 equation:


Simplifying
(4v + 1)(6 + v) = 0

Reorder the terms:
(1 + 4v)(6 + v) = 0

Multiply (1 + 4v) * (6 + v)
(1(6 + v) + 4v * (6 + v)) = 0
((6 * 1 + v * 1) + 4v * (6 + v)) = 0
((6 + 1v) + 4v * (6 + v)) = 0
(6 + 1v + (6 * 4v + v * 4v)) = 0
(6 + 1v + (24v + 4v2)) = 0

Combine like terms: 1v + 24v = 25v
(6 + 25v + 4v2) = 0

Solving
6 + 25v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + v)(1 + 4v) = 0

Subproblem 1

Set the factor '(6 + v)' equal to zero and attempt to solve: Simplifying 6 + v = 0 Solving 6 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + v = 0 + -6 v = 0 + -6 Combine like terms: 0 + -6 = -6 v = -6 Simplifying v = -6

Subproblem 2

Set the factor '(1 + 4v)' equal to zero and attempt to solve: Simplifying 1 + 4v = 0 Solving 1 + 4v = 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 + 4v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4v = 0 + -1 4v = 0 + -1 Combine like terms: 0 + -1 = -1 4v = -1 Divide each side by '4'. v = -0.25 Simplifying v = -0.25

Solution

v = {-6, -0.25}

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