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Simplifying (4v + -1)(v + 3) = 0 Reorder the terms: (-1 + 4v)(v + 3) = 0 Reorder the terms: (-1 + 4v)(3 + v) = 0 Multiply (-1 + 4v) * (3 + v) (-1(3 + v) + 4v * (3 + v)) = 0 ((3 * -1 + v * -1) + 4v * (3 + v)) = 0 ((-3 + -1v) + 4v * (3 + v)) = 0 (-3 + -1v + (3 * 4v + v * 4v)) = 0 (-3 + -1v + (12v + 4v2)) = 0 Combine like terms: -1v + 12v = 11v (-3 + 11v + 4v2) = 0 Solving -3 + 11v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -1v)(1 + -4v) = 0Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 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 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3Subproblem 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 = 0.25Solution
v = {-3, 0.25}
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