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Simplifying 7c(5c + -2) + -2(5c + -2) = 0 Reorder the terms: 7c(-2 + 5c) + -2(5c + -2) = 0 (-2 * 7c + 5c * 7c) + -2(5c + -2) = 0 (-14c + 35c2) + -2(5c + -2) = 0 Reorder the terms: -14c + 35c2 + -2(-2 + 5c) = 0 -14c + 35c2 + (-2 * -2 + 5c * -2) = 0 -14c + 35c2 + (4 + -10c) = 0 Reorder the terms: 4 + -14c + -10c + 35c2 = 0 Combine like terms: -14c + -10c = -24c 4 + -24c + 35c2 = 0 Solving 4 + -24c + 35c2 = 0 Solving for variable 'c'. Factor a trinomial. (2 + -7c)(2 + -5c) = 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 '(2 + -5c)' equal to zero and attempt to solve: Simplifying 2 + -5c = 0 Solving 2 + -5c = 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 + -5c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5c = 0 + -2 -5c = 0 + -2 Combine like terms: 0 + -2 = -2 -5c = -2 Divide each side by '-5'. c = 0.4 Simplifying c = 0.4Solution
c = {0.2857142857, 0.4}
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