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Simplifying (4c + 2)(2c + 7) = 0 Reorder the terms: (2 + 4c)(2c + 7) = 0 Reorder the terms: (2 + 4c)(7 + 2c) = 0 Multiply (2 + 4c) * (7 + 2c) (2(7 + 2c) + 4c * (7 + 2c)) = 0 ((7 * 2 + 2c * 2) + 4c * (7 + 2c)) = 0 ((14 + 4c) + 4c * (7 + 2c)) = 0 (14 + 4c + (7 * 4c + 2c * 4c)) = 0 (14 + 4c + (28c + 8c2)) = 0 Combine like terms: 4c + 28c = 32c (14 + 32c + 8c2) = 0 Solving 14 + 32c + 8c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 16c + 4c2) = 0 Factor a trinomial. 2((7 + 2c)(1 + 2c)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 2c)' equal to zero and attempt to solve: Simplifying 7 + 2c = 0 Solving 7 + 2c = 0 Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2c = 0 + -7 2c = 0 + -7 Combine like terms: 0 + -7 = -7 2c = -7 Divide each side by '2'. c = -3.5 Simplifying c = -3.5Subproblem 2
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 = {-3.5, -0.5}
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