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Simplifying (4c + -3)(5c + -5) = 0 Reorder the terms: (-3 + 4c)(5c + -5) = 0 Reorder the terms: (-3 + 4c)(-5 + 5c) = 0 Multiply (-3 + 4c) * (-5 + 5c) (-3(-5 + 5c) + 4c * (-5 + 5c)) = 0 ((-5 * -3 + 5c * -3) + 4c * (-5 + 5c)) = 0 ((15 + -15c) + 4c * (-5 + 5c)) = 0 (15 + -15c + (-5 * 4c + 5c * 4c)) = 0 (15 + -15c + (-20c + 20c2)) = 0 Combine like terms: -15c + -20c = -35c (15 + -35c + 20c2) = 0 Solving 15 + -35c + 20c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -7c + 4c2) = 0 Factor a trinomial. 5((3 + -4c)(1 + -1c)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -4c)' equal to zero and attempt to solve: Simplifying 3 + -4c = 0 Solving 3 + -4c = 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 + -4c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4c = 0 + -3 -4c = 0 + -3 Combine like terms: 0 + -3 = -3 -4c = -3 Divide each side by '-4'. c = 0.75 Simplifying c = 0.75Subproblem 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 = {0.75, 1}
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