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Simplifying 4rt2 + 48rt + 108r = 0 Reorder the terms: 108r + 48rt + 4rt2 = 0 Solving 108r + 48rt + 4rt2 = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '4r'. 4r(27 + 12t + t2) = 0 Factor a trinomial. 4r((9 + t)(3 + t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(9 + t)' equal to zero and attempt to solve: Simplifying 9 + t = 0 Solving 9 + t = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + t = 0 + -9 t = 0 + -9 Combine like terms: 0 + -9 = -9 t = -9 Add '-1t' to each side of the equation. t + -1t = -9 + -1t Combine like terms: t + -1t = 0 0 = -9 + -1t Simplifying 0 = -9 + -1t The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Add '-1t' to each side of the equation. t + -1t = -3 + -1t Combine like terms: t + -1t = 0 0 = -3 + -1t Simplifying 0 = -3 + -1t The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
r = {0}
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