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Simplifying (2c + -3)(c + 5) = 0 Reorder the terms: (-3 + 2c)(c + 5) = 0 Reorder the terms: (-3 + 2c)(5 + c) = 0 Multiply (-3 + 2c) * (5 + c) (-3(5 + c) + 2c * (5 + c)) = 0 ((5 * -3 + c * -3) + 2c * (5 + c)) = 0 ((-15 + -3c) + 2c * (5 + c)) = 0 (-15 + -3c + (5 * 2c + c * 2c)) = 0 (-15 + -3c + (10c + 2c2)) = 0 Combine like terms: -3c + 10c = 7c (-15 + 7c + 2c2) = 0 Solving -15 + 7c + 2c2 = 0 Solving for variable 'c'. Factor a trinomial. (-5 + -1c)(3 + -2c) = 0Subproblem 1
Set the factor '(-5 + -1c)' equal to zero and attempt to solve: Simplifying -5 + -1c = 0 Solving -5 + -1c = 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 + -1c = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1c = 0 + 5 -1c = 0 + 5 Combine like terms: 0 + 5 = 5 -1c = 5 Divide each side by '-1'. c = -5 Simplifying c = -5Subproblem 2
Set the factor '(3 + -2c)' equal to zero and attempt to solve: Simplifying 3 + -2c = 0 Solving 3 + -2c = 0 Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2c = 0 + -3 -2c = 0 + -3 Combine like terms: 0 + -3 = -3 -2c = -3 Divide each side by '-2'. c = 1.5 Simplifying c = 1.5Solution
c = {-5, 1.5}
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