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Simplifying (8 + v)(4v + -1) = 0 Reorder the terms: (8 + v)(-1 + 4v) = 0 Multiply (8 + v) * (-1 + 4v) (8(-1 + 4v) + v(-1 + 4v)) = 0 ((-1 * 8 + 4v * 8) + v(-1 + 4v)) = 0 ((-8 + 32v) + v(-1 + 4v)) = 0 (-8 + 32v + (-1 * v + 4v * v)) = 0 (-8 + 32v + (-1v + 4v2)) = 0 Combine like terms: 32v + -1v = 31v (-8 + 31v + 4v2) = 0 Solving -8 + 31v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-8 + -1v)(1 + -4v) = 0Subproblem 1
Set the factor '(-8 + -1v)' equal to zero and attempt to solve: Simplifying -8 + -1v = 0 Solving -8 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1v = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1v = 0 + 8 -1v = 0 + 8 Combine like terms: 0 + 8 = 8 -1v = 8 Divide each side by '-1'. v = -8 Simplifying v = -8Subproblem 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 = {-8, 0.25}
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