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Simplifying (2c + -5)(7c + 2) = 0 Reorder the terms: (-5 + 2c)(7c + 2) = 0 Reorder the terms: (-5 + 2c)(2 + 7c) = 0 Multiply (-5 + 2c) * (2 + 7c) (-5(2 + 7c) + 2c * (2 + 7c)) = 0 ((2 * -5 + 7c * -5) + 2c * (2 + 7c)) = 0 ((-10 + -35c) + 2c * (2 + 7c)) = 0 (-10 + -35c + (2 * 2c + 7c * 2c)) = 0 (-10 + -35c + (4c + 14c2)) = 0 Combine like terms: -35c + 4c = -31c (-10 + -31c + 14c2) = 0 Solving -10 + -31c + 14c2 = 0 Solving for variable 'c'. Factor a trinomial. (-2 + -7c)(5 + -2c) = 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 + -2c)' equal to zero and attempt to solve: Simplifying 5 + -2c = 0 Solving 5 + -2c = 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 + -2c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2c = 0 + -5 -2c = 0 + -5 Combine like terms: 0 + -5 = -5 -2c = -5 Divide each side by '-2'. c = 2.5 Simplifying c = 2.5Solution
c = {-0.2857142857, 2.5}
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