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Simplifying (3 + v)(5v + -1) = 0 Reorder the terms: (3 + v)(-1 + 5v) = 0 Multiply (3 + v) * (-1 + 5v) (3(-1 + 5v) + v(-1 + 5v)) = 0 ((-1 * 3 + 5v * 3) + v(-1 + 5v)) = 0 ((-3 + 15v) + v(-1 + 5v)) = 0 (-3 + 15v + (-1 * v + 5v * v)) = 0 (-3 + 15v + (-1v + 5v2)) = 0 Combine like terms: 15v + -1v = 14v (-3 + 14v + 5v2) = 0 Solving -3 + 14v + 5v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -1v)(1 + -5v) = 0Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 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 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3Subproblem 2
Set the factor '(1 + -5v)' equal to zero and attempt to solve: Simplifying 1 + -5v = 0 Solving 1 + -5v = 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 + -5v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5v = 0 + -1 -5v = 0 + -1 Combine like terms: 0 + -1 = -1 -5v = -1 Divide each side by '-5'. v = 0.2 Simplifying v = 0.2Solution
v = {-3, 0.2}
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