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Simplifying 7r3 + 25r2 + -12r = 0 Reorder the terms: -12r + 25r2 + 7r3 = 0 Solving -12r + 25r2 + 7r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-12 + 25r + 7r2) = 0 Factor a trinomial. r((-4 + -1r)(3 + -7r)) = 0Subproblem 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 '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4Subproblem 3
Set the factor '(3 + -7r)' equal to zero and attempt to solve: Simplifying 3 + -7r = 0 Solving 3 + -7r = 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 + -7r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7r = 0 + -3 -7r = 0 + -3 Combine like terms: 0 + -3 = -3 -7r = -3 Divide each side by '-7'. r = 0.4285714286 Simplifying r = 0.4285714286Solution
r = {0, -4, 0.4285714286}
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