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Simplifying (v + -5)(v + 7) = 0 Reorder the terms: (-5 + v)(v + 7) = 0 Reorder the terms: (-5 + v)(7 + v) = 0 Multiply (-5 + v) * (7 + v) (-5(7 + v) + v(7 + v)) = 0 ((7 * -5 + v * -5) + v(7 + v)) = 0 ((-35 + -5v) + v(7 + v)) = 0 (-35 + -5v + (7 * v + v * v)) = 0 (-35 + -5v + (7v + v2)) = 0 Combine like terms: -5v + 7v = 2v (-35 + 2v + v2) = 0 Solving -35 + 2v + v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + -1v)(5 + -1v) = 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 '(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 = 5Solution
v = {-7, 5}
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