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Simplifying c(2c + -1)(4c + 3) = 0 Reorder the terms: c(-1 + 2c)(4c + 3) = 0 Reorder the terms: c(-1 + 2c)(3 + 4c) = 0 Multiply (-1 + 2c) * (3 + 4c) c(-1(3 + 4c) + 2c * (3 + 4c)) = 0 c((3 * -1 + 4c * -1) + 2c * (3 + 4c)) = 0 c((-3 + -4c) + 2c * (3 + 4c)) = 0 c(-3 + -4c + (3 * 2c + 4c * 2c)) = 0 c(-3 + -4c + (6c + 8c2)) = 0 Combine like terms: -4c + 6c = 2c c(-3 + 2c + 8c2) = 0 (-3 * c + 2c * c + 8c2 * c) = 0 (-3c + 2c2 + 8c3) = 0 Solving -3c + 2c2 + 8c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c'. c(-3 + 2c + 8c2) = 0 Factor a trinomial. c((-3 + -4c)(1 + -2c)) = 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 '(-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 = -0.75Subproblem 3
Set the factor '(1 + -2c)' equal to zero and attempt to solve: Simplifying 1 + -2c = 0 Solving 1 + -2c = 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 + -2c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2c = 0 + -1 -2c = 0 + -1 Combine like terms: 0 + -1 = -1 -2c = -1 Divide each side by '-2'. c = 0.5 Simplifying c = 0.5Solution
c = {0, -0.75, 0.5}
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