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Simplifying (4v + -1)(2 + v) = 0 Reorder the terms: (-1 + 4v)(2 + v) = 0 Multiply (-1 + 4v) * (2 + v) (-1(2 + v) + 4v * (2 + v)) = 0 ((2 * -1 + v * -1) + 4v * (2 + v)) = 0 ((-2 + -1v) + 4v * (2 + v)) = 0 (-2 + -1v + (2 * 4v + v * 4v)) = 0 (-2 + -1v + (8v + 4v2)) = 0 Combine like terms: -1v + 8v = 7v (-2 + 7v + 4v2) = 0 Solving -2 + 7v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-2 + -1v)(1 + -4v) = 0Subproblem 1
Set the factor '(-2 + -1v)' equal to zero and attempt to solve: Simplifying -2 + -1v = 0 Solving -2 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1v = 0 + 2 -1v = 0 + 2 Combine like terms: 0 + 2 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2Subproblem 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 = {-2, 0.25}
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