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Simplifying (4c + -6c + 5)(4c + -2c + -1) = 0 Reorder the terms: (5 + 4c + -6c)(4c + -2c + -1) = 0 Combine like terms: 4c + -6c = -2c (5 + -2c)(4c + -2c + -1) = 0 Reorder the terms: (5 + -2c)(-1 + 4c + -2c) = 0 Combine like terms: 4c + -2c = 2c (5 + -2c)(-1 + 2c) = 0 Multiply (5 + -2c) * (-1 + 2c) (5(-1 + 2c) + -2c * (-1 + 2c)) = 0 ((-1 * 5 + 2c * 5) + -2c * (-1 + 2c)) = 0 ((-5 + 10c) + -2c * (-1 + 2c)) = 0 (-5 + 10c + (-1 * -2c + 2c * -2c)) = 0 (-5 + 10c + (2c + -4c2)) = 0 Combine like terms: 10c + 2c = 12c (-5 + 12c + -4c2) = 0 Solving -5 + 12c + -4c2 = 0 Solving for variable 'c'. Factor a trinomial. (-5 + 2c)(1 + -2c) = 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 '(1 + -2c)' equal to zero and attempt to solve: Simplifying 1 + -2c = 0 Solving 1 + -2c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2c = 0 + -1 -2c = 0 + -1 Combine like terms: 0 + -1 = -1 -2c = -1 Divide each side by '-2'. c = 0.5 Simplifying c = 0.5Solution
c = {2.5, 0.5}
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