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Simplifying 2r3 + 6r2t + -56rt2 = 0 Reorder the terms: -56rt2 + 6r2t + 2r3 = 0 Solving -56rt2 + 6r2t + 2r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(-28t2 + 3rt + r2) = 0 Factor a trinomial. 2r((-7t + -1r)(4t + -1r)) = 0 Ignore the factor 2.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 '(-7t + -1r)' equal to zero and attempt to solve: Simplifying -7t + -1r = 0 Reorder the terms: -1r + -7t = 0 Solving -1r + -7t = 0 Move all terms containing r to the left, all other terms to the right. Add '7t' to each side of the equation. -1r + -7t + 7t = 0 + 7t Combine like terms: -7t + 7t = 0 -1r + 0 = 0 + 7t -1r = 0 + 7t Remove the zero: -1r = 7t Divide each side by '-1'. r = -7t Simplifying r = -7tSubproblem 3
Set the factor '(4t + -1r)' equal to zero and attempt to solve: Simplifying 4t + -1r = 0 Reorder the terms: -1r + 4t = 0 Solving -1r + 4t = 0 Move all terms containing r to the left, all other terms to the right. Add '-4t' to each side of the equation. -1r + 4t + -4t = 0 + -4t Combine like terms: 4t + -4t = 0 -1r + 0 = 0 + -4t -1r = 0 + -4t Remove the zero: -1r = -4t Divide each side by '-1'. r = 4t Simplifying r = 4tSolution
r = {0, -7t, 4t}
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