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Simplifying 12r3 + 10r2 + -42r = 0 Reorder the terms: -42r + 10r2 + 12r3 = 0 Solving -42r + 10r2 + 12r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(-21 + 5r + 6r2) = 0 Factor a trinomial. 2r((-7 + -3r)(3 + -2r)) = 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 '(-7 + -3r)' equal to zero and attempt to solve: Simplifying -7 + -3r = 0 Solving -7 + -3r = 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 + -3r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3r = 0 + 7 -3r = 0 + 7 Combine like terms: 0 + 7 = 7 -3r = 7 Divide each side by '-3'. r = -2.333333333 Simplifying r = -2.333333333Subproblem 3
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 = 1.5Solution
r = {0, -2.333333333, 1.5}
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