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Simplifying 3v = 4v(v + 5v) Combine like terms: v + 5v = 6v 3v = 4v(6v) Remove parenthesis around (6v) 3v = 4v * 6v Reorder the terms for easier multiplication: 3v = 4 * 6v * v Multiply 4 * 6 3v = 24v * v Multiply v * v 3v = 24v2 Solving 3v = 24v2 Solving for variable 'v'. Combine like terms: 24v2 + -24v2 = 0 3v + -24v2 = 0 Factor out the Greatest Common Factor (GCF), '3v'. 3v(1 + -8v) = 0 Ignore the factor 3.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 '(1 + -8v)' equal to zero and attempt to solve: Simplifying 1 + -8v = 0 Solving 1 + -8v = 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 + -8v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8v = 0 + -1 -8v = 0 + -1 Combine like terms: 0 + -1 = -1 -8v = -1 Divide each side by '-8'. v = 0.125 Simplifying v = 0.125Solution
v = {0, 0.125}
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