12c^2=27+27c

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Solution for 12c^2=27+27c equation:


Simplifying
12c2 = 27 + 27c

Solving
12c2 = 27 + 27c

Solving for variable 'c'.

Reorder the terms:
-27 + -27c + 12c2 = 27 + 27c + -27 + -27c

Reorder the terms:
-27 + -27c + 12c2 = 27 + -27 + 27c + -27c

Combine like terms: 27 + -27 = 0
-27 + -27c + 12c2 = 0 + 27c + -27c
-27 + -27c + 12c2 = 27c + -27c

Combine like terms: 27c + -27c = 0
-27 + -27c + 12c2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -9c + 4c2) = 0

Factor a trinomial.
3((-3 + -4c)(3 + -1c)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-3 + -4c)' equal to zero and attempt to solve: Simplifying -3 + -4c = 0 Solving -3 + -4c = 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 + -4c = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4c = 0 + 3 -4c = 0 + 3 Combine like terms: 0 + 3 = 3 -4c = 3 Divide each side by '-4'. c = -0.75 Simplifying c = -0.75

Subproblem 2

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 = 3

Solution

c = {-0.75, 3}

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