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Simplifying (5v + -1)(7 + v) = 0 Reorder the terms: (-1 + 5v)(7 + v) = 0 Multiply (-1 + 5v) * (7 + v) (-1(7 + v) + 5v * (7 + v)) = 0 ((7 * -1 + v * -1) + 5v * (7 + v)) = 0 ((-7 + -1v) + 5v * (7 + v)) = 0 (-7 + -1v + (7 * 5v + v * 5v)) = 0 (-7 + -1v + (35v + 5v2)) = 0 Combine like terms: -1v + 35v = 34v (-7 + 34v + 5v2) = 0 Solving -7 + 34v + 5v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + -1v)(1 + -5v) = 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 + -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 = {-7, 0.2}
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