54r^2-216r+192=0

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Solution for 54r^2-216r+192=0 equation:


Simplifying
54r2 + -216r + 192 = 0

Reorder the terms:
192 + -216r + 54r2 = 0

Solving
192 + -216r + 54r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(32 + -36r + 9r2) = 0

Factor a trinomial.
6((4 + -3r)(8 + -3r)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(4 + -3r)' equal to zero and attempt to solve: Simplifying 4 + -3r = 0 Solving 4 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3r = 0 + -4 -3r = 0 + -4 Combine like terms: 0 + -4 = -4 -3r = -4 Divide each side by '-3'. r = 1.333333333 Simplifying r = 1.333333333

Subproblem 2

Set the factor '(8 + -3r)' equal to zero and attempt to solve: Simplifying 8 + -3r = 0 Solving 8 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3r = 0 + -8 -3r = 0 + -8 Combine like terms: 0 + -8 = -8 -3r = -8 Divide each side by '-3'. r = 2.666666667 Simplifying r = 2.666666667

Solution

r = {1.333333333, 2.666666667}

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