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Simplifying (4 + v)(4v + -6) = 0 Reorder the terms: (4 + v)(-6 + 4v) = 0 Multiply (4 + v) * (-6 + 4v) (4(-6 + 4v) + v(-6 + 4v)) = 0 ((-6 * 4 + 4v * 4) + v(-6 + 4v)) = 0 ((-24 + 16v) + v(-6 + 4v)) = 0 (-24 + 16v + (-6 * v + 4v * v)) = 0 (-24 + 16v + (-6v + 4v2)) = 0 Combine like terms: 16v + -6v = 10v (-24 + 10v + 4v2) = 0 Solving -24 + 10v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 5v + 2v2) = 0 Factor a trinomial. 2((-4 + -1v)(3 + -2v)) = 0 Ignore the factor 2.Subproblem 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 '(3 + -2v)' equal to zero and attempt to solve: Simplifying 3 + -2v = 0 Solving 3 + -2v = 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 + -2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2v = 0 + -3 -2v = 0 + -3 Combine like terms: 0 + -3 = -3 -2v = -3 Divide each side by '-2'. v = 1.5 Simplifying v = 1.5Solution
v = {-4, 1.5}
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