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Simplifying (5v + 2)(3 + v) = 0 Reorder the terms: (2 + 5v)(3 + v) = 0 Multiply (2 + 5v) * (3 + v) (2(3 + v) + 5v * (3 + v)) = 0 ((3 * 2 + v * 2) + 5v * (3 + v)) = 0 ((6 + 2v) + 5v * (3 + v)) = 0 (6 + 2v + (3 * 5v + v * 5v)) = 0 (6 + 2v + (15v + 5v2)) = 0 Combine like terms: 2v + 15v = 17v (6 + 17v + 5v2) = 0 Solving 6 + 17v + 5v2 = 0 Solving for variable 'v'. Factor a trinomial. (3 + v)(2 + 5v) = 0Subproblem 1
Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 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 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3Subproblem 2
Set the factor '(2 + 5v)' equal to zero and attempt to solve: Simplifying 2 + 5v = 0 Solving 2 + 5v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5v = 0 + -2 5v = 0 + -2 Combine like terms: 0 + -2 = -2 5v = -2 Divide each side by '5'. v = -0.4 Simplifying v = -0.4Solution
v = {-3, -0.4}
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