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Simplifying (4v2 + 6v + -2)(7V + 3) = 0 Reorder the terms: (-2 + 6v + 4v2)(7V + 3) = 0 Reorder the terms: (-2 + 6v + 4v2)(3 + 7V) = 0 Multiply (-2 + 6v + 4v2) * (3 + 7V) (-2(3 + 7V) + 6v * (3 + 7V) + 4v2 * (3 + 7V)) = 0 ((3 * -2 + 7V * -2) + 6v * (3 + 7V) + 4v2 * (3 + 7V)) = 0 ((-6 + -14V) + 6v * (3 + 7V) + 4v2 * (3 + 7V)) = 0 (-6 + -14V + (3 * 6v + 7V * 6v) + 4v2 * (3 + 7V)) = 0 (-6 + -14V + (18v + 42vV) + 4v2 * (3 + 7V)) = 0 (-6 + -14V + 18v + 42vV + (3 * 4v2 + 7V * 4v2)) = 0 (-6 + -14V + 18v + 42vV + (12v2 + 28v2V)) = 0 (-6 + -14V + 18v + 42vV + 12v2 + 28v2V) = 0 Solving -6 + -14V + 18v + 42vV + 12v2 + 28v2V = 0 Solving for variable 'V'. Move all terms containing V to the left, all other terms to the right. Add '6' to each side of the equation. -6 + -14V + 18v + 42vV + 12v2 + 6 + 28v2V = 0 + 6 Reorder the terms: -6 + 6 + -14V + 18v + 42vV + 12v2 + 28v2V = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -14V + 18v + 42vV + 12v2 + 28v2V = 0 + 6 -14V + 18v + 42vV + 12v2 + 28v2V = 0 + 6 Combine like terms: 0 + 6 = 6 -14V + 18v + 42vV + 12v2 + 28v2V = 6 Add '-18v' to each side of the equation. -14V + 18v + 42vV + 12v2 + -18v + 28v2V = 6 + -18v Reorder the terms: -14V + 18v + -18v + 42vV + 12v2 + 28v2V = 6 + -18v Combine like terms: 18v + -18v = 0 -14V + 0 + 42vV + 12v2 + 28v2V = 6 + -18v -14V + 42vV + 12v2 + 28v2V = 6 + -18v Add '-12v2' to each side of the equation. -14V + 42vV + 12v2 + -12v2 + 28v2V = 6 + -18v + -12v2 Combine like terms: 12v2 + -12v2 = 0 -14V + 42vV + 0 + 28v2V = 6 + -18v + -12v2 -14V + 42vV + 28v2V = 6 + -18v + -12v2 Reorder the terms: -6 + -14V + 18v + 42vV + 12v2 + 28v2V = 6 + -18v + -12v2 + -6 + 18v + 12v2 Reorder the terms: -6 + -14V + 18v + 42vV + 12v2 + 28v2V = 6 + -6 + -18v + 18v + -12v2 + 12v2 Combine like terms: 6 + -6 = 0 -6 + -14V + 18v + 42vV + 12v2 + 28v2V = 0 + -18v + 18v + -12v2 + 12v2 -6 + -14V + 18v + 42vV + 12v2 + 28v2V = -18v + 18v + -12v2 + 12v2 Combine like terms: -18v + 18v = 0 -6 + -14V + 18v + 42vV + 12v2 + 28v2V = 0 + -12v2 + 12v2 -6 + -14V + 18v + 42vV + 12v2 + 28v2V = -12v2 + 12v2 Combine like terms: -12v2 + 12v2 = 0 -6 + -14V + 18v + 42vV + 12v2 + 28v2V = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -7V + 9v + 21vV + 6v2 + 14v2V) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -7V + 9v + 21vV + 6v2 + 14v2V)' equal to zero and attempt to solve: Simplifying -3 + -7V + 9v + 21vV + 6v2 + 14v2V = 0 Solving -3 + -7V + 9v + 21vV + 6v2 + 14v2V = 0 Move all terms containing V to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -7V + 9v + 21vV + 6v2 + 3 + 14v2V = 0 + 3 Reorder the terms: -3 + 3 + -7V + 9v + 21vV + 6v2 + 14v2V = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7V + 9v + 21vV + 6v2 + 14v2V = 0 + 3 -7V + 9v + 21vV + 6v2 + 14v2V = 0 + 3 Combine like terms: 0 + 3 = 3 -7V + 9v + 21vV + 6v2 + 14v2V = 3 Add '-9v' to each side of the equation. -7V + 9v + 21vV + 6v2 + -9v + 14v2V = 3 + -9v Reorder the terms: -7V + 9v + -9v + 21vV + 6v2 + 14v2V = 3 + -9v Combine like terms: 9v + -9v = 0 -7V + 0 + 21vV + 6v2 + 14v2V = 3 + -9v -7V + 21vV + 6v2 + 14v2V = 3 + -9v Add '-6v2' to each side of the equation. -7V + 21vV + 6v2 + -6v2 + 14v2V = 3 + -9v + -6v2 Combine like terms: 6v2 + -6v2 = 0 -7V + 21vV + 0 + 14v2V = 3 + -9v + -6v2 -7V + 21vV + 14v2V = 3 + -9v + -6v2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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