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Simplifying (2v + -1)(4 + -1v) = 0 Reorder the terms: (-1 + 2v)(4 + -1v) = 0 Multiply (-1 + 2v) * (4 + -1v) (-1(4 + -1v) + 2v * (4 + -1v)) = 0 ((4 * -1 + -1v * -1) + 2v * (4 + -1v)) = 0 ((-4 + 1v) + 2v * (4 + -1v)) = 0 (-4 + 1v + (4 * 2v + -1v * 2v)) = 0 (-4 + 1v + (8v + -2v2)) = 0 Combine like terms: 1v + 8v = 9v (-4 + 9v + -2v2) = 0 Solving -4 + 9v + -2v2 = 0 Solving for variable 'v'. Factor a trinomial. (-4 + v)(1 + -2v) = 0Subproblem 1
Set the factor '(-4 + v)' equal to zero and attempt to solve: Simplifying -4 + v = 0 Solving -4 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = 0 + 4 Combine like terms: -4 + 4 = 0 0 + v = 0 + 4 v = 0 + 4 Combine like terms: 0 + 4 = 4 v = 4 Simplifying v = 4Subproblem 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 = 0.5Solution
v = {4, 0.5}
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