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Simplifying (3 + -1v)(4v + -6) = 0 Reorder the terms: (3 + -1v)(-6 + 4v) = 0 Multiply (3 + -1v) * (-6 + 4v) (3(-6 + 4v) + -1v * (-6 + 4v)) = 0 ((-6 * 3 + 4v * 3) + -1v * (-6 + 4v)) = 0 ((-18 + 12v) + -1v * (-6 + 4v)) = 0 (-18 + 12v + (-6 * -1v + 4v * -1v)) = 0 (-18 + 12v + (6v + -4v2)) = 0 Combine like terms: 12v + 6v = 18v (-18 + 18v + -4v2) = 0 Solving -18 + 18v + -4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 9v + -2v2) = 0 Factor a trinomial. 2((-3 + v)(3 + -2v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + v)' equal to zero and attempt to solve: Simplifying -3 + v = 0 Solving -3 + v = 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 + v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + v = 0 + 3 v = 0 + 3 Combine like terms: 0 + 3 = 3 v = 3 Simplifying v = 3Subproblem 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 = {3, 1.5}
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