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Simplifying (7 + v)(2v + -1) = 0 Reorder the terms: (7 + v)(-1 + 2v) = 0 Multiply (7 + v) * (-1 + 2v) (7(-1 + 2v) + v(-1 + 2v)) = 0 ((-1 * 7 + 2v * 7) + v(-1 + 2v)) = 0 ((-7 + 14v) + v(-1 + 2v)) = 0 (-7 + 14v + (-1 * v + 2v * v)) = 0 (-7 + 14v + (-1v + 2v2)) = 0 Combine like terms: 14v + -1v = 13v (-7 + 13v + 2v2) = 0 Solving -7 + 13v + 2v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + -1v)(1 + -2v) = 0Subproblem 1
Set the factor '(-7 + -1v)' equal to zero and attempt to solve: Simplifying -7 + -1v = 0 Solving -7 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1v = 0 + 7 -1v = 0 + 7 Combine like terms: 0 + 7 = 7 -1v = 7 Divide each side by '-1'. v = -7 Simplifying v = -7Subproblem 2
Set the factor '(1 + -2v)' equal to zero and attempt to solve: Simplifying 1 + -2v = 0 Solving 1 + -2v = 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 + -2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2v = 0 + -1 -2v = 0 + -1 Combine like terms: 0 + -1 = -1 -2v = -1 Divide each side by '-2'. v = 0.5 Simplifying v = 0.5Solution
v = {-7, 0.5}
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