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Simplifying 75c2 + 90cp + 27p2 = 0 Reorder the terms: 90cp + 75c2 + 27p2 = 0 Solving 90cp + 75c2 + 27p2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3'. 3(30cp + 25c2 + 9p2) = 0 Factor a trinomial. 3((5c + 3p)(5c + 3p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5c + 3p)' equal to zero and attempt to solve: Simplifying 5c + 3p = 0 Solving 5c + 3p = 0 Move all terms containing c to the left, all other terms to the right. Add '-3p' to each side of the equation. 5c + 3p + -3p = 0 + -3p Combine like terms: 3p + -3p = 0 5c + 0 = 0 + -3p 5c = 0 + -3p Remove the zero: 5c = -3p Divide each side by '5'. c = -0.6p Simplifying c = -0.6pSubproblem 2
Set the factor '(5c + 3p)' equal to zero and attempt to solve: Simplifying 5c + 3p = 0 Solving 5c + 3p = 0 Move all terms containing c to the left, all other terms to the right. Add '-3p' to each side of the equation. 5c + 3p + -3p = 0 + -3p Combine like terms: 3p + -3p = 0 5c + 0 = 0 + -3p 5c = 0 + -3p Remove the zero: 5c = -3p Divide each side by '5'. c = -0.6p Simplifying c = -0.6pSolution
c = {-0.6p, -0.6p}
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