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Simplifying (2c + -5)(3c + -7) = 0 Reorder the terms: (-5 + 2c)(3c + -7) = 0 Reorder the terms: (-5 + 2c)(-7 + 3c) = 0 Multiply (-5 + 2c) * (-7 + 3c) (-5(-7 + 3c) + 2c * (-7 + 3c)) = 0 ((-7 * -5 + 3c * -5) + 2c * (-7 + 3c)) = 0 ((35 + -15c) + 2c * (-7 + 3c)) = 0 (35 + -15c + (-7 * 2c + 3c * 2c)) = 0 (35 + -15c + (-14c + 6c2)) = 0 Combine like terms: -15c + -14c = -29c (35 + -29c + 6c2) = 0 Solving 35 + -29c + 6c2 = 0 Solving for variable 'c'. Factor a trinomial. (7 + -3c)(5 + -2c) = 0Subproblem 1
Set the factor '(7 + -3c)' equal to zero and attempt to solve: Simplifying 7 + -3c = 0 Solving 7 + -3c = 0 Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3c = 0 + -7 -3c = 0 + -7 Combine like terms: 0 + -7 = -7 -3c = -7 Divide each side by '-3'. c = 2.333333333 Simplifying c = 2.333333333Subproblem 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 = {2.333333333, 2.5}
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