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Simplifying 15c3 + 24c3 + -6c2 + 12c = 0 Reorder the terms: 12c + -6c2 + 15c3 + 24c3 = 0 Combine like terms: 15c3 + 24c3 = 39c3 12c + -6c2 + 39c3 = 0 Solving 12c + -6c2 + 39c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3c'. 3c(4 + -2c + 13c2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(4 + -2c + 13c2)' equal to zero and attempt to solve: Simplifying 4 + -2c + 13c2 = 0 Solving 4 + -2c + 13c2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.3076923077 + -0.1538461538c + c2 = 0 Move the constant term to the right: Add '-0.3076923077' to each side of the equation. 0.3076923077 + -0.1538461538c + -0.3076923077 + c2 = 0 + -0.3076923077 Reorder the terms: 0.3076923077 + -0.3076923077 + -0.1538461538c + c2 = 0 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + -0.1538461538c + c2 = 0 + -0.3076923077 -0.1538461538c + c2 = 0 + -0.3076923077 Combine like terms: 0 + -0.3076923077 = -0.3076923077 -0.1538461538c + c2 = -0.3076923077 The c term is -0.1538461538c. Take half its coefficient (-0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. -0.1538461538c + 0.005917159760 + c2 = -0.3076923077 + 0.005917159760 Reorder the terms: 0.005917159760 + -0.1538461538c + c2 = -0.3076923077 + 0.005917159760 Combine like terms: -0.3076923077 + 0.005917159760 = -0.30177514794 0.005917159760 + -0.1538461538c + c2 = -0.30177514794 Factor a perfect square on the left side: (c + -0.0769230769)(c + -0.0769230769) = -0.30177514794 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
c = {0}
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