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Simplifying (8 + v)(4v + -7) = 0 Reorder the terms: (8 + v)(-7 + 4v) = 0 Multiply (8 + v) * (-7 + 4v) (8(-7 + 4v) + v(-7 + 4v)) = 0 ((-7 * 8 + 4v * 8) + v(-7 + 4v)) = 0 ((-56 + 32v) + v(-7 + 4v)) = 0 (-56 + 32v + (-7 * v + 4v * v)) = 0 (-56 + 32v + (-7v + 4v2)) = 0 Combine like terms: 32v + -7v = 25v (-56 + 25v + 4v2) = 0 Solving -56 + 25v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-8 + -1v)(7 + -4v) = 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 + -4v)' equal to zero and attempt to solve: Simplifying 7 + -4v = 0 Solving 7 + -4v = 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 + -4v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4v = 0 + -7 -4v = 0 + -7 Combine like terms: 0 + -7 = -7 -4v = -7 Divide each side by '-4'. v = 1.75 Simplifying v = 1.75Solution
v = {-8, 1.75}
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