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Simplifying (2v + -7)(2 + -1v) = 0 Reorder the terms: (-7 + 2v)(2 + -1v) = 0 Multiply (-7 + 2v) * (2 + -1v) (-7(2 + -1v) + 2v * (2 + -1v)) = 0 ((2 * -7 + -1v * -7) + 2v * (2 + -1v)) = 0 ((-14 + 7v) + 2v * (2 + -1v)) = 0 (-14 + 7v + (2 * 2v + -1v * 2v)) = 0 (-14 + 7v + (4v + -2v2)) = 0 Combine like terms: 7v + 4v = 11v (-14 + 11v + -2v2) = 0 Solving -14 + 11v + -2v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + 2v)(2 + -1v) = 0Subproblem 1
Set the factor '(-7 + 2v)' equal to zero and attempt to solve: Simplifying -7 + 2v = 0 Solving -7 + 2v = 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 + 2v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2v = 0 + 7 2v = 0 + 7 Combine like terms: 0 + 7 = 7 2v = 7 Divide each side by '2'. v = 3.5 Simplifying v = 3.5Subproblem 2
Set the factor '(2 + -1v)' equal to zero and attempt to solve: Simplifying 2 + -1v = 0 Solving 2 + -1v = 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 + -1v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1v = 0 + -2 -1v = 0 + -2 Combine like terms: 0 + -2 = -2 -1v = -2 Divide each side by '-1'. v = 2 Simplifying v = 2Solution
v = {3.5, 2}
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