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Simplifying 3c(5c + -2) + -13(5c + -2) = 0 Reorder the terms: 3c(-2 + 5c) + -13(5c + -2) = 0 (-2 * 3c + 5c * 3c) + -13(5c + -2) = 0 (-6c + 15c2) + -13(5c + -2) = 0 Reorder the terms: -6c + 15c2 + -13(-2 + 5c) = 0 -6c + 15c2 + (-2 * -13 + 5c * -13) = 0 -6c + 15c2 + (26 + -65c) = 0 Reorder the terms: 26 + -6c + -65c + 15c2 = 0 Combine like terms: -6c + -65c = -71c 26 + -71c + 15c2 = 0 Solving 26 + -71c + 15c2 = 0 Solving for variable 'c'. Factor a trinomial. (2 + -5c)(13 + -3c) = 0Subproblem 1
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 = 0.4Subproblem 2
Set the factor '(13 + -3c)' equal to zero and attempt to solve: Simplifying 13 + -3c = 0 Solving 13 + -3c = 0 Move all terms containing c to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -3c = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -3c = 0 + -13 -3c = 0 + -13 Combine like terms: 0 + -13 = -13 -3c = -13 Divide each side by '-3'. c = 4.333333333 Simplifying c = 4.333333333Solution
c = {0.4, 4.333333333}
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