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Simplifying 4c(9c + -4)(4c + -1) = 0 Reorder the terms: 4c(-4 + 9c)(4c + -1) = 0 Reorder the terms: 4c(-4 + 9c)(-1 + 4c) = 0 Multiply (-4 + 9c) * (-1 + 4c) 4c(-4(-1 + 4c) + 9c * (-1 + 4c)) = 0 4c((-1 * -4 + 4c * -4) + 9c * (-1 + 4c)) = 0 4c((4 + -16c) + 9c * (-1 + 4c)) = 0 4c(4 + -16c + (-1 * 9c + 4c * 9c)) = 0 4c(4 + -16c + (-9c + 36c2)) = 0 Combine like terms: -16c + -9c = -25c 4c(4 + -25c + 36c2) = 0 (4 * 4c + -25c * 4c + 36c2 * 4c) = 0 (16c + -100c2 + 144c3) = 0 Solving 16c + -100c2 + 144c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4c'. 4c(4 + -25c + 36c2) = 0 Factor a trinomial. 4c((1 + -4c)(4 + -9c)) = 0 Ignore the factor 4.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 + -4c)' equal to zero and attempt to solve: Simplifying 1 + -4c = 0 Solving 1 + -4c = 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 + -4c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4c = 0 + -1 -4c = 0 + -1 Combine like terms: 0 + -1 = -1 -4c = -1 Divide each side by '-4'. c = 0.25 Simplifying c = 0.25Subproblem 3
Set the factor '(4 + -9c)' equal to zero and attempt to solve: Simplifying 4 + -9c = 0 Solving 4 + -9c = 0 Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -9c = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9c = 0 + -4 -9c = 0 + -4 Combine like terms: 0 + -4 = -4 -9c = -4 Divide each side by '-9'. c = 0.4444444444 Simplifying c = 0.4444444444Solution
c = {0, 0.25, 0.4444444444}
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