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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 = -24c (-14 + -24c + 8c2) = 0 Solving -14 + -24c + 8c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -12c + 4c2) = 0 Factor a trinomial. 2((-1 + -2c)(7 + -2c)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.5Subproblem 2
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 = 3.5Solution
c = {-0.5, 3.5}
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