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Simplifying (3v + -18)(18v + -3) = 0 Reorder the terms: (-18 + 3v)(18v + -3) = 0 Reorder the terms: (-18 + 3v)(-3 + 18v) = 0 Multiply (-18 + 3v) * (-3 + 18v) (-18(-3 + 18v) + 3v * (-3 + 18v)) = 0 ((-3 * -18 + 18v * -18) + 3v * (-3 + 18v)) = 0 ((54 + -324v) + 3v * (-3 + 18v)) = 0 (54 + -324v + (-3 * 3v + 18v * 3v)) = 0 (54 + -324v + (-9v + 54v2)) = 0 Combine like terms: -324v + -9v = -333v (54 + -333v + 54v2) = 0 Solving 54 + -333v + 54v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '9'. 9(6 + -37v + 6v2) = 0 Factor a trinomial. 9((1 + -6v)(6 + -1v)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -6v)' equal to zero and attempt to solve: Simplifying 1 + -6v = 0 Solving 1 + -6v = 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 + -6v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6v = 0 + -1 -6v = 0 + -1 Combine like terms: 0 + -1 = -1 -6v = -1 Divide each side by '-6'. v = 0.1666666667 Simplifying v = 0.1666666667Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve: Simplifying 6 + -1v = 0 Solving 6 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1v = 0 + -6 -1v = 0 + -6 Combine like terms: 0 + -6 = -6 -1v = -6 Divide each side by '-1'. v = 6 Simplifying v = 6Solution
v = {0.1666666667, 6}
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