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Simplifying (4c + -5)(7c + -2) = 0 Reorder the terms: (-5 + 4c)(7c + -2) = 0 Reorder the terms: (-5 + 4c)(-2 + 7c) = 0 Multiply (-5 + 4c) * (-2 + 7c) (-5(-2 + 7c) + 4c * (-2 + 7c)) = 0 ((-2 * -5 + 7c * -5) + 4c * (-2 + 7c)) = 0 ((10 + -35c) + 4c * (-2 + 7c)) = 0 (10 + -35c + (-2 * 4c + 7c * 4c)) = 0 (10 + -35c + (-8c + 28c2)) = 0 Combine like terms: -35c + -8c = -43c (10 + -43c + 28c2) = 0 Solving 10 + -43c + 28c2 = 0 Solving for variable 'c'. Factor a trinomial. (2 + -7c)(5 + -4c) = 0Subproblem 1
Set the factor '(2 + -7c)' equal to zero and attempt to solve: Simplifying 2 + -7c = 0 Solving 2 + -7c = 0 Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7c = 0 + -2 -7c = 0 + -2 Combine like terms: 0 + -2 = -2 -7c = -2 Divide each side by '-7'. c = 0.2857142857 Simplifying c = 0.2857142857Subproblem 2
Set the factor '(5 + -4c)' equal to zero and attempt to solve: Simplifying 5 + -4c = 0 Solving 5 + -4c = 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 + -4c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4c = 0 + -5 -4c = 0 + -5 Combine like terms: 0 + -5 = -5 -4c = -5 Divide each side by '-4'. c = 1.25 Simplifying c = 1.25Solution
c = {0.2857142857, 1.25}
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