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Simplifying c2 + -4c = 30 + 3c Reorder the terms: -4c + c2 = 30 + 3c Solving -4c + c2 = 30 + 3c Solving for variable 'c'. Reorder the terms: -30 + -4c + -3c + c2 = 30 + 3c + -30 + -3c Combine like terms: -4c + -3c = -7c -30 + -7c + c2 = 30 + 3c + -30 + -3c Reorder the terms: -30 + -7c + c2 = 30 + -30 + 3c + -3c Combine like terms: 30 + -30 = 0 -30 + -7c + c2 = 0 + 3c + -3c -30 + -7c + c2 = 3c + -3c Combine like terms: 3c + -3c = 0 -30 + -7c + c2 = 0 Factor a trinomial. (-3 + -1c)(10 + -1c) = 0Subproblem 1
Set the factor '(-3 + -1c)' equal to zero and attempt to solve: Simplifying -3 + -1c = 0 Solving -3 + -1c = 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 + -1c = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1c = 0 + 3 -1c = 0 + 3 Combine like terms: 0 + 3 = 3 -1c = 3 Divide each side by '-1'. c = -3 Simplifying c = -3Subproblem 2
Set the factor '(10 + -1c)' equal to zero and attempt to solve: Simplifying 10 + -1c = 0 Solving 10 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1c = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1c = 0 + -10 -1c = 0 + -10 Combine like terms: 0 + -10 = -10 -1c = -10 Divide each side by '-1'. c = 10 Simplifying c = 10Solution
c = {-3, 10}
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