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Simplifying 20w2 + 13wc + -15c2 = 0 Reorder the terms: 13cw + -15c2 + 20w2 = 0 Solving 13cw + -15c2 + 20w2 = 0 Solving for variable 'c'. Factor a trinomial. (-5c + -4w)(3c + -5w) = 0Subproblem 1
Set the factor '(-5c + -4w)' equal to zero and attempt to solve: Simplifying -5c + -4w = 0 Solving -5c + -4w = 0 Move all terms containing c to the left, all other terms to the right. Add '4w' to each side of the equation. -5c + -4w + 4w = 0 + 4w Combine like terms: -4w + 4w = 0 -5c + 0 = 0 + 4w -5c = 0 + 4w Remove the zero: -5c = 4w Divide each side by '-5'. c = -0.8w Simplifying c = -0.8wSubproblem 2
Set the factor '(3c + -5w)' equal to zero and attempt to solve: Simplifying 3c + -5w = 0 Solving 3c + -5w = 0 Move all terms containing c to the left, all other terms to the right. Add '5w' to each side of the equation. 3c + -5w + 5w = 0 + 5w Combine like terms: -5w + 5w = 0 3c + 0 = 0 + 5w 3c = 0 + 5w Remove the zero: 3c = 5w Divide each side by '3'. c = 1.666666667w Simplifying c = 1.666666667wSolution
c = {-0.8w, 1.666666667w}
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