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Simplifying 20r4 + 136r3 + 180r2 = 0 Reorder the terms: 180r2 + 136r3 + 20r4 = 0 Solving 180r2 + 136r3 + 20r4 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4r2'. 4r2(45 + 34r + 5r2) = 0 Factor a trinomial. 4r2((5 + r)(9 + 5r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r2 = 0 Take the square root of each side: r = {0}Subproblem 2
Set the factor '(5 + r)' equal to zero and attempt to solve: Simplifying 5 + r = 0 Solving 5 + r = 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 + r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + r = 0 + -5 r = 0 + -5 Combine like terms: 0 + -5 = -5 r = -5 Simplifying r = -5Subproblem 3
Set the factor '(9 + 5r)' equal to zero and attempt to solve: Simplifying 9 + 5r = 0 Solving 9 + 5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5r = 0 + -9 5r = 0 + -9 Combine like terms: 0 + -9 = -9 5r = -9 Divide each side by '5'. r = -1.8 Simplifying r = -1.8Solution
r = {0, -5, -1.8}
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