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Simplifying (9v + 7)(2v + -6) = 0 Reorder the terms: (7 + 9v)(2v + -6) = 0 Reorder the terms: (7 + 9v)(-6 + 2v) = 0 Multiply (7 + 9v) * (-6 + 2v) (7(-6 + 2v) + 9v * (-6 + 2v)) = 0 ((-6 * 7 + 2v * 7) + 9v * (-6 + 2v)) = 0 ((-42 + 14v) + 9v * (-6 + 2v)) = 0 (-42 + 14v + (-6 * 9v + 2v * 9v)) = 0 (-42 + 14v + (-54v + 18v2)) = 0 Combine like terms: 14v + -54v = -40v (-42 + -40v + 18v2) = 0 Solving -42 + -40v + 18v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -20v + 9v2) = 0 Factor a trinomial. 2((-7 + -9v)(3 + -1v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -9v)' equal to zero and attempt to solve: Simplifying -7 + -9v = 0 Solving -7 + -9v = 0 Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -9v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -9v = 0 + 7 -9v = 0 + 7 Combine like terms: 0 + 7 = 7 -9v = 7 Divide each side by '-9'. v = -0.7777777778 Simplifying v = -0.7777777778Subproblem 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 = {-0.7777777778, 3}
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