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Simplifying -2(3v + -1) * 3v = 8 + 2(6v + -6) Reorder the terms: -2(-1 + 3v) * 3v = 8 + 2(6v + -6) Reorder the terms for easier multiplication: -2 * 3v(-1 + 3v) = 8 + 2(6v + -6) Multiply -2 * 3 -6v(-1 + 3v) = 8 + 2(6v + -6) (-1 * -6v + 3v * -6v) = 8 + 2(6v + -6) (6v + -18v2) = 8 + 2(6v + -6) Reorder the terms: 6v + -18v2 = 8 + 2(-6 + 6v) 6v + -18v2 = 8 + (-6 * 2 + 6v * 2) 6v + -18v2 = 8 + (-12 + 12v) Combine like terms: 8 + -12 = -4 6v + -18v2 = -4 + 12v Solving 6v + -18v2 = -4 + 12v Solving for variable 'v'. Reorder the terms: 4 + 6v + -12v + -18v2 = -4 + 12v + 4 + -12v Combine like terms: 6v + -12v = -6v 4 + -6v + -18v2 = -4 + 12v + 4 + -12v Reorder the terms: 4 + -6v + -18v2 = -4 + 4 + 12v + -12v Combine like terms: -4 + 4 = 0 4 + -6v + -18v2 = 0 + 12v + -12v 4 + -6v + -18v2 = 12v + -12v Combine like terms: 12v + -12v = 0 4 + -6v + -18v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -3v + -9v2) = 0 Factor a trinomial. 2((1 + -3v)(2 + 3v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -3v)' equal to zero and attempt to solve: Simplifying 1 + -3v = 0 Solving 1 + -3v = 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 + -3v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3v = 0 + -1 -3v = 0 + -1 Combine like terms: 0 + -1 = -1 -3v = -1 Divide each side by '-3'. v = 0.3333333333 Simplifying v = 0.3333333333Subproblem 2
Set the factor '(2 + 3v)' equal to zero and attempt to solve: Simplifying 2 + 3v = 0 Solving 2 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3v = 0 + -2 3v = 0 + -2 Combine like terms: 0 + -2 = -2 3v = -2 Divide each side by '3'. v = -0.6666666667 Simplifying v = -0.6666666667Solution
v = {0.3333333333, -0.6666666667}
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