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Simplifying (4v + -5)(5v + 5) = 0 Reorder the terms: (-5 + 4v)(5v + 5) = 0 Reorder the terms: (-5 + 4v)(5 + 5v) = 0 Multiply (-5 + 4v) * (5 + 5v) (-5(5 + 5v) + 4v * (5 + 5v)) = 0 ((5 * -5 + 5v * -5) + 4v * (5 + 5v)) = 0 ((-25 + -25v) + 4v * (5 + 5v)) = 0 (-25 + -25v + (5 * 4v + 5v * 4v)) = 0 (-25 + -25v + (20v + 20v2)) = 0 Combine like terms: -25v + 20v = -5v (-25 + -5v + 20v2) = 0 Solving -25 + -5v + 20v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + -1v + 4v2) = 0 Factor a trinomial. 5((-1 + -1v)(5 + -4v)) = 0 Ignore the factor 5.Subproblem 1
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 = -1Subproblem 2
Set the factor '(5 + -4v)' equal to zero and attempt to solve: Simplifying 5 + -4v = 0 Solving 5 + -4v = 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 + -4v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4v = 0 + -5 -4v = 0 + -5 Combine like terms: 0 + -5 = -5 -4v = -5 Divide each side by '-4'. v = 1.25 Simplifying v = 1.25Solution
v = {-1, 1.25}
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