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Simplifying 27 = v(v + -6) Reorder the terms: 27 = v(-6 + v) 27 = (-6 * v + v * v) 27 = (-6v + v2) Solving 27 = -6v + v2 Solving for variable 'v'. Reorder the terms: 27 + 6v + -1v2 = -6v + 6v + v2 + -1v2 Combine like terms: -6v + 6v = 0 27 + 6v + -1v2 = 0 + v2 + -1v2 27 + 6v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 27 + 6v + -1v2 = 0 Factor a trinomial. (9 + -1v)(3 + v) = 0Subproblem 1
Set the factor '(9 + -1v)' equal to zero and attempt to solve: Simplifying 9 + -1v = 0 Solving 9 + -1v = 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 + -1v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1v = 0 + -9 -1v = 0 + -9 Combine like terms: 0 + -9 = -9 -1v = -9 Divide each side by '-1'. v = 9 Simplifying v = 9Subproblem 2
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 = -3Solution
v = {9, -3}
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