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Simplifying 3c(4c + -3)(3c + -1) = 0 Reorder the terms: 3c(-3 + 4c)(3c + -1) = 0 Reorder the terms: 3c(-3 + 4c)(-1 + 3c) = 0 Multiply (-3 + 4c) * (-1 + 3c) 3c(-3(-1 + 3c) + 4c * (-1 + 3c)) = 0 3c((-1 * -3 + 3c * -3) + 4c * (-1 + 3c)) = 0 3c((3 + -9c) + 4c * (-1 + 3c)) = 0 3c(3 + -9c + (-1 * 4c + 3c * 4c)) = 0 3c(3 + -9c + (-4c + 12c2)) = 0 Combine like terms: -9c + -4c = -13c 3c(3 + -13c + 12c2) = 0 (3 * 3c + -13c * 3c + 12c2 * 3c) = 0 (9c + -39c2 + 36c3) = 0 Solving 9c + -39c2 + 36c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3c'. 3c(3 + -13c + 12c2) = 0 Factor a trinomial. 3c((1 + -3c)(3 + -4c)) = 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 '(1 + -3c)' equal to zero and attempt to solve: Simplifying 1 + -3c = 0 Solving 1 + -3c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3c = 0 + -1 -3c = 0 + -1 Combine like terms: 0 + -1 = -1 -3c = -1 Divide each side by '-3'. c = 0.3333333333 Simplifying c = 0.3333333333Subproblem 3
Set the factor '(3 + -4c)' equal to zero and attempt to solve: Simplifying 3 + -4c = 0 Solving 3 + -4c = 0 Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4c = 0 + -3 -4c = 0 + -3 Combine like terms: 0 + -3 = -3 -4c = -3 Divide each side by '-4'. c = 0.75 Simplifying c = 0.75Solution
c = {0, 0.3333333333, 0.75}
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