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Simplifying c(2 + -5c) = (2c + -3) * c (2 * c + -5c * c) = (2c + -3) * c (2c + -5c2) = (2c + -3) * c Reorder the terms: 2c + -5c2 = (-3 + 2c) * c Reorder the terms for easier multiplication: 2c + -5c2 = c(-3 + 2c) 2c + -5c2 = (-3 * c + 2c * c) 2c + -5c2 = (-3c + 2c2) Solving 2c + -5c2 = -3c + 2c2 Solving for variable 'c'. Reorder the terms: 2c + 3c + -5c2 + -2c2 = -3c + 2c2 + 3c + -2c2 Combine like terms: 2c + 3c = 5c 5c + -5c2 + -2c2 = -3c + 2c2 + 3c + -2c2 Combine like terms: -5c2 + -2c2 = -7c2 5c + -7c2 = -3c + 2c2 + 3c + -2c2 Reorder the terms: 5c + -7c2 = -3c + 3c + 2c2 + -2c2 Combine like terms: -3c + 3c = 0 5c + -7c2 = 0 + 2c2 + -2c2 5c + -7c2 = 2c2 + -2c2 Combine like terms: 2c2 + -2c2 = 0 5c + -7c2 = 0 Factor out the Greatest Common Factor (GCF), 'c'. c(5 + -7c) = 0Subproblem 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 '(5 + -7c)' equal to zero and attempt to solve: Simplifying 5 + -7c = 0 Solving 5 + -7c = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7c = 0 + -5 -7c = 0 + -5 Combine like terms: 0 + -5 = -5 -7c = -5 Divide each side by '-7'. c = 0.7142857143 Simplifying c = 0.7142857143Solution
c = {0, 0.7142857143}
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