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Simplifying (4 + -1v)(5v + 7) = 0 Reorder the terms: (4 + -1v)(7 + 5v) = 0 Multiply (4 + -1v) * (7 + 5v) (4(7 + 5v) + -1v * (7 + 5v)) = 0 ((7 * 4 + 5v * 4) + -1v * (7 + 5v)) = 0 ((28 + 20v) + -1v * (7 + 5v)) = 0 (28 + 20v + (7 * -1v + 5v * -1v)) = 0 (28 + 20v + (-7v + -5v2)) = 0 Combine like terms: 20v + -7v = 13v (28 + 13v + -5v2) = 0 Solving 28 + 13v + -5v2 = 0 Solving for variable 'v'. Factor a trinomial. (4 + -1v)(7 + 5v) = 0Subproblem 1
Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4Subproblem 2
Set the factor '(7 + 5v)' equal to zero and attempt to solve: Simplifying 7 + 5v = 0 Solving 7 + 5v = 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 + 5v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5v = 0 + -7 5v = 0 + -7 Combine like terms: 0 + -7 = -7 5v = -7 Divide each side by '5'. v = -1.4 Simplifying v = -1.4Solution
v = {4, -1.4}
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