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Simplifying (8v + -1)(4v + 1) = 0 Reorder the terms: (-1 + 8v)(4v + 1) = 0 Reorder the terms: (-1 + 8v)(1 + 4v) = 0 Multiply (-1 + 8v) * (1 + 4v) (-1(1 + 4v) + 8v * (1 + 4v)) = 0 ((1 * -1 + 4v * -1) + 8v * (1 + 4v)) = 0 ((-1 + -4v) + 8v * (1 + 4v)) = 0 (-1 + -4v + (1 * 8v + 4v * 8v)) = 0 (-1 + -4v + (8v + 32v2)) = 0 Combine like terms: -4v + 8v = 4v (-1 + 4v + 32v2) = 0 Solving -1 + 4v + 32v2 = 0 Solving for variable 'v'. Factor a trinomial. (-1 + -4v)(1 + -8v) = 0Subproblem 1
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 = -0.25Subproblem 2
Set the factor '(1 + -8v)' equal to zero and attempt to solve: Simplifying 1 + -8v = 0 Solving 1 + -8v = 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 + -8v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8v = 0 + -1 -8v = 0 + -1 Combine like terms: 0 + -1 = -1 -8v = -1 Divide each side by '-8'. v = 0.125 Simplifying v = 0.125Solution
v = {-0.25, 0.125}
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