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Simplifying 2c(c + -3)(7c + 9) = 0 Reorder the terms: 2c(-3 + c)(7c + 9) = 0 Reorder the terms: 2c(-3 + c)(9 + 7c) = 0 Multiply (-3 + c) * (9 + 7c) 2c(-3(9 + 7c) + c(9 + 7c)) = 0 2c((9 * -3 + 7c * -3) + c(9 + 7c)) = 0 2c((-27 + -21c) + c(9 + 7c)) = 0 2c(-27 + -21c + (9 * c + 7c * c)) = 0 2c(-27 + -21c + (9c + 7c2)) = 0 Combine like terms: -21c + 9c = -12c 2c(-27 + -12c + 7c2) = 0 (-27 * 2c + -12c * 2c + 7c2 * 2c) = 0 (-54c + -24c2 + 14c3) = 0 Solving -54c + -24c2 + 14c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2c'. 2c(-27 + -12c + 7c2) = 0 Factor a trinomial. 2c((-9 + -7c)(3 + -1c)) = 0 Ignore the factor 2.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 '(-9 + -7c)' equal to zero and attempt to solve: Simplifying -9 + -7c = 0 Solving -9 + -7c = 0 Move all terms containing c to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -7c = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -7c = 0 + 9 -7c = 0 + 9 Combine like terms: 0 + 9 = 9 -7c = 9 Divide each side by '-7'. c = -1.285714286 Simplifying c = -1.285714286Subproblem 3
Set the factor '(3 + -1c)' equal to zero and attempt to solve: Simplifying 3 + -1c = 0 Solving 3 + -1c = 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 + -1c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1c = 0 + -3 -1c = 0 + -3 Combine like terms: 0 + -3 = -3 -1c = -3 Divide each side by '-1'. c = 3 Simplifying c = 3Solution
c = {0, -1.285714286, 3}
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