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Simplifying 12c4 + 36c3 + 15c2 = 0 Reorder the terms: 15c2 + 36c3 + 12c4 = 0 Solving 15c2 + 36c3 + 12c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3c2'. 3c2(5 + 12c + 4c2) = 0 Factor a trinomial. 3c2((5 + 2c)(1 + 2c)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'c2' equal to zero and attempt to solve: Simplifying c2 = 0 Solving c2 = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c2 = 0 Take the square root of each side: c = {0}Subproblem 2
Set the factor '(5 + 2c)' equal to zero and attempt to solve: Simplifying 5 + 2c = 0 Solving 5 + 2c = 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 + 2c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2c = 0 + -5 2c = 0 + -5 Combine like terms: 0 + -5 = -5 2c = -5 Divide each side by '2'. c = -2.5 Simplifying c = -2.5Subproblem 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, -2.5, -0.5}
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