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Simplifying (5c + -4)(6c + -6) = 0 Reorder the terms: (-4 + 5c)(6c + -6) = 0 Reorder the terms: (-4 + 5c)(-6 + 6c) = 0 Multiply (-4 + 5c) * (-6 + 6c) (-4(-6 + 6c) + 5c * (-6 + 6c)) = 0 ((-6 * -4 + 6c * -4) + 5c * (-6 + 6c)) = 0 ((24 + -24c) + 5c * (-6 + 6c)) = 0 (24 + -24c + (-6 * 5c + 6c * 5c)) = 0 (24 + -24c + (-30c + 30c2)) = 0 Combine like terms: -24c + -30c = -54c (24 + -54c + 30c2) = 0 Solving 24 + -54c + 30c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '6'. 6(4 + -9c + 5c2) = 0 Factor a trinomial. 6((4 + -5c)(1 + -1c)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + -5c)' equal to zero and attempt to solve: Simplifying 4 + -5c = 0 Solving 4 + -5c = 0 Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5c = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5c = 0 + -4 -5c = 0 + -4 Combine like terms: 0 + -4 = -4 -5c = -4 Divide each side by '-5'. c = 0.8 Simplifying c = 0.8Subproblem 2
Set the factor '(1 + -1c)' equal to zero and attempt to solve: Simplifying 1 + -1c = 0 Solving 1 + -1c = 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 + -1c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1c = 0 + -1 -1c = 0 + -1 Combine like terms: 0 + -1 = -1 -1c = -1 Divide each side by '-1'. c = 1 Simplifying c = 1Solution
c = {0.8, 1}
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