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Simplifying (3c + -2)(2c + 5) = 0 Reorder the terms: (-2 + 3c)(2c + 5) = 0 Reorder the terms: (-2 + 3c)(5 + 2c) = 0 Multiply (-2 + 3c) * (5 + 2c) (-2(5 + 2c) + 3c * (5 + 2c)) = 0 ((5 * -2 + 2c * -2) + 3c * (5 + 2c)) = 0 ((-10 + -4c) + 3c * (5 + 2c)) = 0 (-10 + -4c + (5 * 3c + 2c * 3c)) = 0 (-10 + -4c + (15c + 6c2)) = 0 Combine like terms: -4c + 15c = 11c (-10 + 11c + 6c2) = 0 Solving -10 + 11c + 6c2 = 0 Solving for variable 'c'. Factor a trinomial. (-5 + -2c)(2 + -3c) = 0Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(2 + -3c)' equal to zero and attempt to solve: Simplifying 2 + -3c = 0 Solving 2 + -3c = 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 + -3c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3c = 0 + -2 -3c = 0 + -2 Combine like terms: 0 + -2 = -2 -3c = -2 Divide each side by '-3'. c = 0.6666666667 Simplifying c = 0.6666666667Solution
c = {-2.5, 0.6666666667}
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