27k^2-144k+189=0

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Solution for 27k^2-144k+189=0 equation:


Simplifying
27k2 + -144k + 189 = 0

Reorder the terms:
189 + -144k + 27k2 = 0

Solving
189 + -144k + 27k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '9'.
9(21 + -16k + 3k2) = 0

Factor a trinomial.
9((7 + -3k)(3 + -1k)) = 0

Ignore the factor 9.

Subproblem 1

Set the factor '(7 + -3k)' equal to zero and attempt to solve: Simplifying 7 + -3k = 0 Solving 7 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3k = 0 + -7 -3k = 0 + -7 Combine like terms: 0 + -7 = -7 -3k = -7 Divide each side by '-3'. k = 2.333333333 Simplifying k = 2.333333333

Subproblem 2

Set the factor '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3

Solution

k = {2.333333333, 3}

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