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Simplifying (9v + 5)(4v + -12) = 0 Reorder the terms: (5 + 9v)(4v + -12) = 0 Reorder the terms: (5 + 9v)(-12 + 4v) = 0 Multiply (5 + 9v) * (-12 + 4v) (5(-12 + 4v) + 9v * (-12 + 4v)) = 0 ((-12 * 5 + 4v * 5) + 9v * (-12 + 4v)) = 0 ((-60 + 20v) + 9v * (-12 + 4v)) = 0 (-60 + 20v + (-12 * 9v + 4v * 9v)) = 0 (-60 + 20v + (-108v + 36v2)) = 0 Combine like terms: 20v + -108v = -88v (-60 + -88v + 36v2) = 0 Solving -60 + -88v + 36v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -22v + 9v2) = 0 Factor a trinomial. 4((-5 + -9v)(3 + -1v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -9v)' equal to zero and attempt to solve: Simplifying -5 + -9v = 0 Solving -5 + -9v = 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 + -9v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -9v = 0 + 5 -9v = 0 + 5 Combine like terms: 0 + 5 = 5 -9v = 5 Divide each side by '-9'. v = -0.5555555556 Simplifying v = -0.5555555556Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 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 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Solution
v = {-0.5555555556, 3}
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