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Simplifying (3v + -7)(8 + v) = 0 Reorder the terms: (-7 + 3v)(8 + v) = 0 Multiply (-7 + 3v) * (8 + v) (-7(8 + v) + 3v * (8 + v)) = 0 ((8 * -7 + v * -7) + 3v * (8 + v)) = 0 ((-56 + -7v) + 3v * (8 + v)) = 0 (-56 + -7v + (8 * 3v + v * 3v)) = 0 (-56 + -7v + (24v + 3v2)) = 0 Combine like terms: -7v + 24v = 17v (-56 + 17v + 3v2) = 0 Solving -56 + 17v + 3v2 = 0 Solving for variable 'v'. Factor a trinomial. (-8 + -1v)(7 + -3v) = 0Subproblem 1
Set the factor '(-8 + -1v)' equal to zero and attempt to solve: Simplifying -8 + -1v = 0 Solving -8 + -1v = 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 + -1v = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1v = 0 + 8 -1v = 0 + 8 Combine like terms: 0 + 8 = 8 -1v = 8 Divide each side by '-1'. v = -8 Simplifying v = -8Subproblem 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 = {-8, 2.333333333}
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