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Simplifying (3v + -2)(5 + v) = 0 Reorder the terms: (-2 + 3v)(5 + v) = 0 Multiply (-2 + 3v) * (5 + v) (-2(5 + v) + 3v * (5 + v)) = 0 ((5 * -2 + v * -2) + 3v * (5 + v)) = 0 ((-10 + -2v) + 3v * (5 + v)) = 0 (-10 + -2v + (5 * 3v + v * 3v)) = 0 (-10 + -2v + (15v + 3v2)) = 0 Combine like terms: -2v + 15v = 13v (-10 + 13v + 3v2) = 0 Solving -10 + 13v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (-5 + -1v)(2 + -3v) = 0Subproblem 1
Set the factor '(-5 + -1v)' equal to zero and attempt to solve: Simplifying -5 + -1v = 0 Solving -5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1v = 0 + 5 -1v = 0 + 5 Combine like terms: 0 + 5 = 5 -1v = 5 Divide each side by '-1'. v = -5 Simplifying v = -5Subproblem 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 = {-5, 0.6666666667}
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