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Simplifying (3v + -8)(2 + v) = 0 Reorder the terms: (-8 + 3v)(2 + v) = 0 Multiply (-8 + 3v) * (2 + v) (-8(2 + v) + 3v * (2 + v)) = 0 ((2 * -8 + v * -8) + 3v * (2 + v)) = 0 ((-16 + -8v) + 3v * (2 + v)) = 0 (-16 + -8v + (2 * 3v + v * 3v)) = 0 (-16 + -8v + (6v + 3v2)) = 0 Combine like terms: -8v + 6v = -2v (-16 + -2v + 3v2) = 0 Solving -16 + -2v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (-2 + -1v)(8 + -3v) = 0Subproblem 1
Set the factor '(-2 + -1v)' equal to zero and attempt to solve: Simplifying -2 + -1v = 0 Solving -2 + -1v = 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 + -1v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1v = 0 + 2 -1v = 0 + 2 Combine like terms: 0 + 2 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2Subproblem 2
Set the factor '(8 + -3v)' equal to zero and attempt to solve: Simplifying 8 + -3v = 0 Solving 8 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3v = 0 + -8 -3v = 0 + -8 Combine like terms: 0 + -8 = -8 -3v = -8 Divide each side by '-3'. v = 2.666666667 Simplifying v = 2.666666667Solution
v = {-2, 2.666666667}
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