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Simplifying 4rt2 + 28rt + 40r = 0 Reorder the terms: 40r + 28rt + 4rt2 = 0 Solving 40r + 28rt + 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(10 + 7t + t2) = 0 Factor a trinomial. 4r((5 + t)(2 + 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 '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Add '-1t' to each side of the equation. t + -1t = -5 + -1t Combine like terms: t + -1t = 0 0 = -5 + -1t Simplifying 0 = -5 + -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 '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Add '-1t' to each side of the equation. t + -1t = -2 + -1t Combine like terms: t + -1t = 0 0 = -2 + -1t Simplifying 0 = -2 + -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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