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Simplifying 10r3 = 66r2 + 28r Reorder the terms: 10r3 = 28r + 66r2 Solving 10r3 = 28r + 66r2 Solving for variable 'r'. Reorder the terms: -28r + -66r2 + 10r3 = 28r + 66r2 + -28r + -66r2 Reorder the terms: -28r + -66r2 + 10r3 = 28r + -28r + 66r2 + -66r2 Combine like terms: 28r + -28r = 0 -28r + -66r2 + 10r3 = 0 + 66r2 + -66r2 -28r + -66r2 + 10r3 = 66r2 + -66r2 Combine like terms: 66r2 + -66r2 = 0 -28r + -66r2 + 10r3 = 0 Factor out the Greatest Common Factor (GCF), '2r'. 2r(-14 + -33r + 5r2) = 0 Factor a trinomial. 2r((-2 + -5r)(7 + -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 '(-2 + -5r)' equal to zero and attempt to solve: Simplifying -2 + -5r = 0 Solving -2 + -5r = 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 + -5r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5r = 0 + 2 -5r = 0 + 2 Combine like terms: 0 + 2 = 2 -5r = 2 Divide each side by '-5'. r = -0.4 Simplifying r = -0.4Subproblem 3
Set the factor '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7Solution
r = {0, -0.4, 7}
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