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Simplifying (4c + -2)(c + 4) = 0 Reorder the terms: (-2 + 4c)(c + 4) = 0 Reorder the terms: (-2 + 4c)(4 + c) = 0 Multiply (-2 + 4c) * (4 + c) (-2(4 + c) + 4c * (4 + c)) = 0 ((4 * -2 + c * -2) + 4c * (4 + c)) = 0 ((-8 + -2c) + 4c * (4 + c)) = 0 (-8 + -2c + (4 * 4c + c * 4c)) = 0 (-8 + -2c + (16c + 4c2)) = 0 Combine like terms: -2c + 16c = 14c (-8 + 14c + 4c2) = 0 Solving -8 + 14c + 4c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 7c + 2c2) = 0 Factor a trinomial. 2((-4 + -1c)(1 + -2c)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1c)' equal to zero and attempt to solve: Simplifying -4 + -1c = 0 Solving -4 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1c = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1c = 0 + 4 -1c = 0 + 4 Combine like terms: 0 + 4 = 4 -1c = 4 Divide each side by '-1'. c = -4 Simplifying c = -4Subproblem 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 = {-4, 0.5}
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