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Simplifying (2v + 3)(4 + -1v) = 0 Reorder the terms: (3 + 2v)(4 + -1v) = 0 Multiply (3 + 2v) * (4 + -1v) (3(4 + -1v) + 2v * (4 + -1v)) = 0 ((4 * 3 + -1v * 3) + 2v * (4 + -1v)) = 0 ((12 + -3v) + 2v * (4 + -1v)) = 0 (12 + -3v + (4 * 2v + -1v * 2v)) = 0 (12 + -3v + (8v + -2v2)) = 0 Combine like terms: -3v + 8v = 5v (12 + 5v + -2v2) = 0 Solving 12 + 5v + -2v2 = 0 Solving for variable 'v'. Factor a trinomial. (4 + -1v)(3 + 2v) = 0Subproblem 1
Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 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 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4Subproblem 2
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 = -1.5Solution
v = {4, -1.5}
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