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Simplifying (5 + -1v)(2v + 3) = 0 Reorder the terms: (5 + -1v)(3 + 2v) = 0 Multiply (5 + -1v) * (3 + 2v) (5(3 + 2v) + -1v * (3 + 2v)) = 0 ((3 * 5 + 2v * 5) + -1v * (3 + 2v)) = 0 ((15 + 10v) + -1v * (3 + 2v)) = 0 (15 + 10v + (3 * -1v + 2v * -1v)) = 0 (15 + 10v + (-3v + -2v2)) = 0 Combine like terms: 10v + -3v = 7v (15 + 7v + -2v2) = 0 Solving 15 + 7v + -2v2 = 0 Solving for variable 'v'. Factor a trinomial. (5 + -1v)(3 + 2v) = 0Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Subproblem 2
Set the factor '(3 + 2v)' equal to zero and attempt to solve: Simplifying 3 + 2v = 0 Solving 3 + 2v = 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 + 2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2v = 0 + -3 2v = 0 + -3 Combine like terms: 0 + -3 = -3 2v = -3 Divide each side by '2'. v = -1.5 Simplifying v = -1.5Solution
v = {5, -1.5}
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