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Simplifying (9 + -1v)(4v + -2) = 0 Reorder the terms: (9 + -1v)(-2 + 4v) = 0 Multiply (9 + -1v) * (-2 + 4v) (9(-2 + 4v) + -1v * (-2 + 4v)) = 0 ((-2 * 9 + 4v * 9) + -1v * (-2 + 4v)) = 0 ((-18 + 36v) + -1v * (-2 + 4v)) = 0 (-18 + 36v + (-2 * -1v + 4v * -1v)) = 0 (-18 + 36v + (2v + -4v2)) = 0 Combine like terms: 36v + 2v = 38v (-18 + 38v + -4v2) = 0 Solving -18 + 38v + -4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 19v + -2v2) = 0 Factor a trinomial. 2((-9 + v)(1 + -2v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + v)' equal to zero and attempt to solve: Simplifying -9 + v = 0 Solving -9 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + v = 0 + 9 v = 0 + 9 Combine like terms: 0 + 9 = 9 v = 9 Simplifying v = 9Subproblem 2
Set the factor '(1 + -2v)' equal to zero and attempt to solve: Simplifying 1 + -2v = 0 Solving 1 + -2v = 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 + -2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2v = 0 + -1 -2v = 0 + -1 Combine like terms: 0 + -1 = -1 -2v = -1 Divide each side by '-2'. v = 0.5 Simplifying v = 0.5Solution
v = {9, 0.5}
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