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Simplifying (-4c + -36)(c + 4) = 0 Reorder the terms: (-36 + -4c)(c + 4) = 0 Reorder the terms: (-36 + -4c)(4 + c) = 0 Multiply (-36 + -4c) * (4 + c) (-36(4 + c) + -4c * (4 + c)) = 0 ((4 * -36 + c * -36) + -4c * (4 + c)) = 0 ((-144 + -36c) + -4c * (4 + c)) = 0 (-144 + -36c + (4 * -4c + c * -4c)) = 0 (-144 + -36c + (-16c + -4c2)) = 0 Combine like terms: -36c + -16c = -52c (-144 + -52c + -4c2) = 0 Solving -144 + -52c + -4c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '-4'. -4(36 + 13c + c2) = 0 Factor a trinomial. -4((9 + c)(4 + c)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(9 + c)' equal to zero and attempt to solve: Simplifying 9 + c = 0 Solving 9 + c = 0 Move all terms containing c to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + c = 0 + -9 Combine like terms: 9 + -9 = 0 0 + c = 0 + -9 c = 0 + -9 Combine like terms: 0 + -9 = -9 c = -9 Simplifying c = -9Subproblem 2
Set the factor '(4 + c)' equal to zero and attempt to solve: Simplifying 4 + c = 0 Solving 4 + c = 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 + c = 0 + -4 Combine like terms: 4 + -4 = 0 0 + c = 0 + -4 c = 0 + -4 Combine like terms: 0 + -4 = -4 c = -4 Simplifying c = -4Solution
c = {-9, -4}
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