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Simplifying (v + -7)(v + 5) = 0 Reorder the terms: (-7 + v)(v + 5) = 0 Reorder the terms: (-7 + v)(5 + v) = 0 Multiply (-7 + v) * (5 + v) (-7(5 + v) + v(5 + v)) = 0 ((5 * -7 + v * -7) + v(5 + v)) = 0 ((-35 + -7v) + v(5 + v)) = 0 (-35 + -7v + (5 * v + v * v)) = 0 (-35 + -7v + (5v + v2)) = 0 Combine like terms: -7v + 5v = -2v (-35 + -2v + v2) = 0 Solving -35 + -2v + 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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