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Simplifying (3v + -7)(2v + -6) = 0 Reorder the terms: (-7 + 3v)(2v + -6) = 0 Reorder the terms: (-7 + 3v)(-6 + 2v) = 0 Multiply (-7 + 3v) * (-6 + 2v) (-7(-6 + 2v) + 3v * (-6 + 2v)) = 0 ((-6 * -7 + 2v * -7) + 3v * (-6 + 2v)) = 0 ((42 + -14v) + 3v * (-6 + 2v)) = 0 (42 + -14v + (-6 * 3v + 2v * 3v)) = 0 (42 + -14v + (-18v + 6v2)) = 0 Combine like terms: -14v + -18v = -32v (42 + -32v + 6v2) = 0 Solving 42 + -32v + 6v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + -16v + 3v2) = 0 Factor a trinomial. 2((7 + -3v)(3 + -1v)) = 0 Ignore the factor 2.Subproblem 1
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 = 2.333333333Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 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 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Solution
v = {2.333333333, 3}
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