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Simplifying (4 + v)(5v + -7) = 0 Reorder the terms: (4 + v)(-7 + 5v) = 0 Multiply (4 + v) * (-7 + 5v) (4(-7 + 5v) + v(-7 + 5v)) = 0 ((-7 * 4 + 5v * 4) + v(-7 + 5v)) = 0 ((-28 + 20v) + v(-7 + 5v)) = 0 (-28 + 20v + (-7 * v + 5v * v)) = 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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