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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 = -12v (35 + -12v + v2) = 0 Solving 35 + -12v + v2 = 0 Solving for variable 'v'. Factor a trinomial. (5 + -1v)(7 + -1v) = 0Subproblem 1
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 = 5Subproblem 2
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 = 7Solution
v = {5, 7}
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