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Simplifying (4r + 7r2) + -1(6r3 + -6r) = 0 Remove parenthesis around (4r + 7r2) 4r + 7r2 + -1(6r3 + -6r) = 0 Reorder the terms: 4r + 7r2 + -1(-6r + 6r3) = 0 4r + 7r2 + (-6r * -1 + 6r3 * -1) = 0 4r + 7r2 + (6r + -6r3) = 0 Reorder the terms: 4r + 6r + 7r2 + -6r3 = 0 Combine like terms: 4r + 6r = 10r 10r + 7r2 + -6r3 = 0 Solving 10r + 7r2 + -6r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(10 + 7r + -6r2) = 0 Factor a trinomial. r((2 + -1r)(5 + 6r)) = 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 '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 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 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2Subproblem 3
Set the factor '(5 + 6r)' equal to zero and attempt to solve: Simplifying 5 + 6r = 0 Solving 5 + 6r = 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 + 6r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6r = 0 + -5 6r = 0 + -5 Combine like terms: 0 + -5 = -5 6r = -5 Divide each side by '6'. r = -0.8333333333 Simplifying r = -0.8333333333Solution
r = {0, 2, -0.8333333333}
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