12c^2+36ct+27t^2=

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Solution for 12c^2+36ct+27t^2= equation:


Simplifying
12c2 + 36ct + 27t2 = 0

Reorder the terms:
36ct + 12c2 + 27t2 = 0

Solving
36ct + 12c2 + 27t2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12ct + 4c2 + 9t2) = 0

Factor a trinomial.
3((2c + 3t)(2c + 3t)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(2c + 3t)' equal to zero and attempt to solve: Simplifying 2c + 3t = 0 Solving 2c + 3t = 0 Move all terms containing c to the left, all other terms to the right. Add '-3t' to each side of the equation. 2c + 3t + -3t = 0 + -3t Combine like terms: 3t + -3t = 0 2c + 0 = 0 + -3t 2c = 0 + -3t Remove the zero: 2c = -3t Divide each side by '2'. c = -1.5t Simplifying c = -1.5t

Subproblem 2

Set the factor '(2c + 3t)' equal to zero and attempt to solve: Simplifying 2c + 3t = 0 Solving 2c + 3t = 0 Move all terms containing c to the left, all other terms to the right. Add '-3t' to each side of the equation. 2c + 3t + -3t = 0 + -3t Combine like terms: 3t + -3t = 0 2c + 0 = 0 + -3t 2c = 0 + -3t Remove the zero: 2c = -3t Divide each side by '2'. c = -1.5t Simplifying c = -1.5t

Solution

c = {-1.5t, -1.5t}

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