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Simplifying (7 + -1v)(3v + 1) = 0 Reorder the terms: (7 + -1v)(1 + 3v) = 0 Multiply (7 + -1v) * (1 + 3v) (7(1 + 3v) + -1v * (1 + 3v)) = 0 ((1 * 7 + 3v * 7) + -1v * (1 + 3v)) = 0 ((7 + 21v) + -1v * (1 + 3v)) = 0 (7 + 21v + (1 * -1v + 3v * -1v)) = 0 (7 + 21v + (-1v + -3v2)) = 0 Combine like terms: 21v + -1v = 20v (7 + 20v + -3v2) = 0 Solving 7 + 20v + -3v2 = 0 Solving for variable 'v'. Factor a trinomial. (7 + -1v)(1 + 3v) = 0Subproblem 1
Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7Subproblem 2
Set the factor '(1 + 3v)' equal to zero and attempt to solve: Simplifying 1 + 3v = 0 Solving 1 + 3v = 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 + 3v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3v = 0 + -1 3v = 0 + -1 Combine like terms: 0 + -1 = -1 3v = -1 Divide each side by '3'. v = -0.3333333333 Simplifying v = -0.3333333333Solution
v = {7, -0.3333333333}
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