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Simplifying (6 + -1v)(3v + 7) = 0 Reorder the terms: (6 + -1v)(7 + 3v) = 0 Multiply (6 + -1v) * (7 + 3v) (6(7 + 3v) + -1v * (7 + 3v)) = 0 ((7 * 6 + 3v * 6) + -1v * (7 + 3v)) = 0 ((42 + 18v) + -1v * (7 + 3v)) = 0 (42 + 18v + (7 * -1v + 3v * -1v)) = 0 (42 + 18v + (-7v + -3v2)) = 0 Combine like terms: 18v + -7v = 11v (42 + 11v + -3v2) = 0 Solving 42 + 11v + -3v2 = 0 Solving for variable 'v'. Factor a trinomial. (6 + -1v)(7 + 3v) = 0Subproblem 1
Set the factor '(6 + -1v)' equal to zero and attempt to solve: Simplifying 6 + -1v = 0 Solving 6 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1v = 0 + -6 -1v = 0 + -6 Combine like terms: 0 + -6 = -6 -1v = -6 Divide each side by '-1'. v = 6 Simplifying v = 6Subproblem 2
Set the factor '(7 + 3v)' equal to zero and attempt to solve: Simplifying 7 + 3v = 0 Solving 7 + 3v = 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 + 3v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3v = 0 + -7 3v = 0 + -7 Combine like terms: 0 + -7 = -7 3v = -7 Divide each side by '3'. v = -2.333333333 Simplifying v = -2.333333333Solution
v = {6, -2.333333333}
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