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Simplifying 50r4 + 145r3 + 105r2 = 0 Reorder the terms: 105r2 + 145r3 + 50r4 = 0 Solving 105r2 + 145r3 + 50r4 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5r2'. 5r2(21 + 29r + 10r2) = 0 Factor a trinomial. 5r2((3 + 2r)(7 + 5r)) = 0 Ignore the factor 5.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 '(3 + 2r)' equal to zero and attempt to solve: Simplifying 3 + 2r = 0 Solving 3 + 2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2r = 0 + -3 2r = 0 + -3 Combine like terms: 0 + -3 = -3 2r = -3 Divide each side by '2'. r = -1.5 Simplifying r = -1.5Subproblem 3
Set the factor '(7 + 5r)' equal to zero and attempt to solve: Simplifying 7 + 5r = 0 Solving 7 + 5r = 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 + 5r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5r = 0 + -7 5r = 0 + -7 Combine like terms: 0 + -7 = -7 5r = -7 Divide each side by '5'. r = -1.4 Simplifying r = -1.4Solution
r = {0, -1.5, -1.4}
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