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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 = 13v (-6 + 13v + 5v2) = 0 Solving -6 + 13v + 5v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -1v)(2 + -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 '(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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