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Simplifying 20r2 + -53rt + -21t2 = 0 Reorder the terms: -53rt + 20r2 + -21t2 = 0 Solving -53rt + 20r2 + -21t2 = 0 Solving for variable 'r'. Factor a trinomial. (r + -3t)(20r + 7t) = 0Subproblem 1
Set the factor '(r + -3t)' equal to zero and attempt to solve: Simplifying r + -3t = 0 Solving r + -3t = 0 Move all terms containing r to the left, all other terms to the right. Add '3t' to each side of the equation. r + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 r + 0 = 0 + 3t r = 0 + 3t Remove the zero: r = 3t Simplifying r = 3tSubproblem 2
Set the factor '(20r + 7t)' equal to zero and attempt to solve: Simplifying 20r + 7t = 0 Solving 20r + 7t = 0 Move all terms containing r to the left, all other terms to the right. Add '-7t' to each side of the equation. 20r + 7t + -7t = 0 + -7t Combine like terms: 7t + -7t = 0 20r + 0 = 0 + -7t 20r = 0 + -7t Remove the zero: 20r = -7t Divide each side by '20'. r = -0.35t Simplifying r = -0.35tSolution
r = {3t, -0.35t}
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