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Simplifying 3r3 + 12r2t + -36rt2 = 0 Reorder the terms: -36rt2 + 12r2t + 3r3 = 0 Solving -36rt2 + 12r2t + 3r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3r'. 3r(-12t2 + 4rt + r2) = 0 Factor a trinomial. 3r((-6t + -1r)(2t + -1r)) = 0 Ignore the factor 3.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 '(-6t + -1r)' equal to zero and attempt to solve: Simplifying -6t + -1r = 0 Reorder the terms: -1r + -6t = 0 Solving -1r + -6t = 0 Move all terms containing r to the left, all other terms to the right. Add '6t' to each side of the equation. -1r + -6t + 6t = 0 + 6t Combine like terms: -6t + 6t = 0 -1r + 0 = 0 + 6t -1r = 0 + 6t Remove the zero: -1r = 6t Divide each side by '-1'. r = -6t Simplifying r = -6tSubproblem 3
Set the factor '(2t + -1r)' equal to zero and attempt to solve: Simplifying 2t + -1r = 0 Reorder the terms: -1r + 2t = 0 Solving -1r + 2t = 0 Move all terms containing r to the left, all other terms to the right. Add '-2t' to each side of the equation. -1r + 2t + -2t = 0 + -2t Combine like terms: 2t + -2t = 0 -1r + 0 = 0 + -2t -1r = 0 + -2t Remove the zero: -1r = -2t Divide each side by '-1'. r = 2t Simplifying r = 2tSolution
r = {0, -6t, 2t}
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