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Simplifying 6r2t + 7rt2 + t3 = 0 Reorder the terms: 7rt2 + 6r2t + t3 = 0 Solving 7rt2 + 6r2t + t3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 't'. t(7rt + 6r2 + t2) = 0 Factor a trinomial. t((6r + t)(r + t)) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing r to the left, all other terms to the right. Add '-1t' to each side of the equation. t + -1t = 0 + -1t Remove the zero: 0 = -1t Simplifying 0 = -1t The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(6r + t)' equal to zero and attempt to solve: Simplifying 6r + t = 0 Solving 6r + t = 0 Move all terms containing r to the left, all other terms to the right. Add '-1t' to each side of the equation. 6r + t + -1t = 0 + -1t Combine like terms: t + -1t = 0 6r + 0 = 0 + -1t 6r = 0 + -1t Remove the zero: 6r = -1t Divide each side by '6'. r = -0.1666666667t Simplifying r = -0.1666666667tSubproblem 3
Set the factor '(r + t)' equal to zero and attempt to solve: Simplifying r + t = 0 Solving r + t = 0 Move all terms containing r to the left, all other terms to the right. Add '-1t' to each side of the equation. r + t + -1t = 0 + -1t Combine like terms: t + -1t = 0 r + 0 = 0 + -1t r = 0 + -1t Remove the zero: r = -1t Simplifying r = -1tSolution
r = {-0.1666666667t, -1t}
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