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Simplifying (3 + v)(3v + -2) = 0 Reorder the terms: (3 + v)(-2 + 3v) = 0 Multiply (3 + v) * (-2 + 3v) (3(-2 + 3v) + v(-2 + 3v)) = 0 ((-2 * 3 + 3v * 3) + v(-2 + 3v)) = 0 ((-6 + 9v) + v(-2 + 3v)) = 0 (-6 + 9v + (-2 * v + 3v * v)) = 0 (-6 + 9v + (-2v + 3v2)) = 0 Combine like terms: 9v + -2v = 7v (-6 + 7v + 3v2) = 0 Solving -6 + 7v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -1v)(2 + -3v) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(2 + -3v)' equal to zero and attempt to solve: Simplifying 2 + -3v = 0 Solving 2 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3v = 0 + -2 -3v = 0 + -2 Combine like terms: 0 + -2 = -2 -3v = -2 Divide each side by '-3'. v = 0.6666666667 Simplifying v = 0.6666666667Solution
v = {-3, 0.6666666667}
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