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Simplifying (4v + -3)(5v + -5) = 0 Reorder the terms: (-3 + 4v)(5v + -5) = 0 Reorder the terms: (-3 + 4v)(-5 + 5v) = 0 Multiply (-3 + 4v) * (-5 + 5v) (-3(-5 + 5v) + 4v * (-5 + 5v)) = 0 ((-5 * -3 + 5v * -3) + 4v * (-5 + 5v)) = 0 ((15 + -15v) + 4v * (-5 + 5v)) = 0 (15 + -15v + (-5 * 4v + 5v * 4v)) = 0 (15 + -15v + (-20v + 20v2)) = 0 Combine like terms: -15v + -20v = -35v (15 + -35v + 20v2) = 0 Solving 15 + -35v + 20v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -7v + 4v2) = 0 Factor a trinomial. 5((3 + -4v)(1 + -1v)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -4v)' equal to zero and attempt to solve: Simplifying 3 + -4v = 0 Solving 3 + -4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4v = 0 + -3 -4v = 0 + -3 Combine like terms: 0 + -3 = -3 -4v = -3 Divide each side by '-4'. v = 0.75 Simplifying v = 0.75Subproblem 2
Set the factor '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1Solution
v = {0.75, 1}
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