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Simplifying -7v(v + 2) + 2v + 6 = 7v + 6 Reorder the terms: -7v(2 + v) + 2v + 6 = 7v + 6 (2 * -7v + v * -7v) + 2v + 6 = 7v + 6 (-14v + -7v2) + 2v + 6 = 7v + 6 Reorder the terms: 6 + -14v + 2v + -7v2 = 7v + 6 Combine like terms: -14v + 2v = -12v 6 + -12v + -7v2 = 7v + 6 Reorder the terms: 6 + -12v + -7v2 = 6 + 7v Add '-6' to each side of the equation. 6 + -12v + -6 + -7v2 = 6 + -6 + 7v Reorder the terms: 6 + -6 + -12v + -7v2 = 6 + -6 + 7v Combine like terms: 6 + -6 = 0 0 + -12v + -7v2 = 6 + -6 + 7v -12v + -7v2 = 6 + -6 + 7v Combine like terms: 6 + -6 = 0 -12v + -7v2 = 0 + 7v -12v + -7v2 = 7v Solving -12v + -7v2 = 7v Solving for variable 'v'. Reorder the terms: -12v + -7v + -7v2 = 7v + -7v Combine like terms: -12v + -7v = -19v -19v + -7v2 = 7v + -7v Combine like terms: 7v + -7v = 0 -19v + -7v2 = 0 Factor out the Greatest Common Factor (GCF), '-1v'. -1v(19 + 7v) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(19 + 7v)' equal to zero and attempt to solve: Simplifying 19 + 7v = 0 Solving 19 + 7v = 0 Move all terms containing v to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 7v = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 7v = 0 + -19 7v = 0 + -19 Combine like terms: 0 + -19 = -19 7v = -19 Divide each side by '7'. v = -2.714285714 Simplifying v = -2.714285714Solution
v = {0, -2.714285714}
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