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Simplifying (5c + -1)(7c + -4) = 0 Reorder the terms: (-1 + 5c)(7c + -4) = 0 Reorder the terms: (-1 + 5c)(-4 + 7c) = 0 Multiply (-1 + 5c) * (-4 + 7c) (-1(-4 + 7c) + 5c * (-4 + 7c)) = 0 ((-4 * -1 + 7c * -1) + 5c * (-4 + 7c)) = 0 ((4 + -7c) + 5c * (-4 + 7c)) = 0 (4 + -7c + (-4 * 5c + 7c * 5c)) = 0 (4 + -7c + (-20c + 35c2)) = 0 Combine like terms: -7c + -20c = -27c (4 + -27c + 35c2) = 0 Solving 4 + -27c + 35c2 = 0 Solving for variable 'c'. Factor a trinomial. (1 + -5c)(4 + -7c) = 0Subproblem 1
Set the factor '(1 + -5c)' equal to zero and attempt to solve: Simplifying 1 + -5c = 0 Solving 1 + -5c = 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 + -5c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5c = 0 + -1 -5c = 0 + -1 Combine like terms: 0 + -1 = -1 -5c = -1 Divide each side by '-5'. c = 0.2 Simplifying c = 0.2Subproblem 2
Set the factor '(4 + -7c)' equal to zero and attempt to solve: Simplifying 4 + -7c = 0 Solving 4 + -7c = 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 + -7c = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7c = 0 + -4 -7c = 0 + -4 Combine like terms: 0 + -4 = -4 -7c = -4 Divide each side by '-7'. c = 0.5714285714 Simplifying c = 0.5714285714Solution
c = {0.2, 0.5714285714}
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