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Simplifying 12v2 + -36vw + -48w2 = 0 Reorder the terms: -36vw + 12v2 + -48w2 = 0 Solving -36vw + 12v2 + -48w2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '12'. 12(-3vw + v2 + -4w2) = 0 Factor a trinomial. 12((v + -4w)(v + w)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(v + -4w)' equal to zero and attempt to solve: Simplifying v + -4w = 0 Solving v + -4w = 0 Move all terms containing v to the left, all other terms to the right. Add '4w' to each side of the equation. v + -4w + 4w = 0 + 4w Combine like terms: -4w + 4w = 0 v + 0 = 0 + 4w v = 0 + 4w Remove the zero: v = 4w Simplifying v = 4wSubproblem 2
Set the factor '(v + w)' equal to zero and attempt to solve: Simplifying v + w = 0 Solving v + w = 0 Move all terms containing v to the left, all other terms to the right. Add '-1w' to each side of the equation. v + w + -1w = 0 + -1w Combine like terms: w + -1w = 0 v + 0 = 0 + -1w v = 0 + -1w Remove the zero: v = -1w Simplifying v = -1wSolution
v = {4w, -1w}
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