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Simplifying (3 + -1v)(5v + 1) = 0 Reorder the terms: (3 + -1v)(1 + 5v) = 0 Multiply (3 + -1v) * (1 + 5v) (3(1 + 5v) + -1v * (1 + 5v)) = 0 ((1 * 3 + 5v * 3) + -1v * (1 + 5v)) = 0 ((3 + 15v) + -1v * (1 + 5v)) = 0 (3 + 15v + (1 * -1v + 5v * -1v)) = 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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