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Simplifying (2v + 3)(4v + -1) = 0 Reorder the terms: (3 + 2v)(4v + -1) = 0 Reorder the terms: (3 + 2v)(-1 + 4v) = 0 Multiply (3 + 2v) * (-1 + 4v) (3(-1 + 4v) + 2v * (-1 + 4v)) = 0 ((-1 * 3 + 4v * 3) + 2v * (-1 + 4v)) = 0 ((-3 + 12v) + 2v * (-1 + 4v)) = 0 (-3 + 12v + (-1 * 2v + 4v * 2v)) = 0 (-3 + 12v + (-2v + 8v2)) = 0 Combine like terms: 12v + -2v = 10v (-3 + 10v + 8v2) = 0 Solving -3 + 10v + 8v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -2v)(1 + -4v) = 0Subproblem 1
Set the factor '(-3 + -2v)' equal to zero and attempt to solve: Simplifying -3 + -2v = 0 Solving -3 + -2v = 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 + -2v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2v = 0 + 3 -2v = 0 + 3 Combine like terms: 0 + 3 = 3 -2v = 3 Divide each side by '-2'. v = -1.5 Simplifying v = -1.5Subproblem 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 = {-1.5, 0.25}
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