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Simplifying 12c2 + -26ct + -126t2 = 0 Reorder the terms: -26ct + 12c2 + -126t2 = 0 Solving -26ct + 12c2 + -126t2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13ct + 6c2 + -63t2) = 0 Factor a trinomial. 2((2c + -9t)(3c + 7t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2c + -9t)' equal to zero and attempt to solve: Simplifying 2c + -9t = 0 Solving 2c + -9t = 0 Move all terms containing c to the left, all other terms to the right. Add '9t' to each side of the equation. 2c + -9t + 9t = 0 + 9t Combine like terms: -9t + 9t = 0 2c + 0 = 0 + 9t 2c = 0 + 9t Remove the zero: 2c = 9t Divide each side by '2'. c = 4.5t Simplifying c = 4.5tSubproblem 2
Set the factor '(3c + 7t)' equal to zero and attempt to solve: Simplifying 3c + 7t = 0 Solving 3c + 7t = 0 Move all terms containing c to the left, all other terms to the right. Add '-7t' to each side of the equation. 3c + 7t + -7t = 0 + -7t Combine like terms: 7t + -7t = 0 3c + 0 = 0 + -7t 3c = 0 + -7t Remove the zero: 3c = -7t Divide each side by '3'. c = -2.333333333t Simplifying c = -2.333333333tSolution
c = {4.5t, -2.333333333t}
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