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Simplifying (7v + -7)(8v + -6) = 0 Reorder the terms: (-7 + 7v)(8v + -6) = 0 Reorder the terms: (-7 + 7v)(-6 + 8v) = 0 Multiply (-7 + 7v) * (-6 + 8v) (-7(-6 + 8v) + 7v * (-6 + 8v)) = 0 ((-6 * -7 + 8v * -7) + 7v * (-6 + 8v)) = 0 ((42 + -56v) + 7v * (-6 + 8v)) = 0 (42 + -56v + (-6 * 7v + 8v * 7v)) = 0 (42 + -56v + (-42v + 56v2)) = 0 Combine like terms: -56v + -42v = -98v (42 + -98v + 56v2) = 0 Solving 42 + -98v + 56v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '14'. 14(3 + -7v + 4v2) = 0 Factor a trinomial. 14((3 + -4v)(1 + -1v)) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(3 + -4v)' equal to zero and attempt to solve: Simplifying 3 + -4v = 0 Solving 3 + -4v = 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 + -4v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4v = 0 + -3 -4v = 0 + -3 Combine like terms: 0 + -3 = -3 -4v = -3 Divide each side by '-4'. v = 0.75 Simplifying v = 0.75Subproblem 2
Set the factor '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1Solution
v = {0.75, 1}
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