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Simplifying 3r2 + 23r + -165 = 5r + -3r2 + 3 Reorder the terms: -165 + 23r + 3r2 = 5r + -3r2 + 3 Reorder the terms: -165 + 23r + 3r2 = 3 + 5r + -3r2 Solving -165 + 23r + 3r2 = 3 + 5r + -3r2 Solving for variable 'r'. Reorder the terms: -165 + -3 + 23r + -5r + 3r2 + 3r2 = 3 + 5r + -3r2 + -3 + -5r + 3r2 Combine like terms: -165 + -3 = -168 -168 + 23r + -5r + 3r2 + 3r2 = 3 + 5r + -3r2 + -3 + -5r + 3r2 Combine like terms: 23r + -5r = 18r -168 + 18r + 3r2 + 3r2 = 3 + 5r + -3r2 + -3 + -5r + 3r2 Combine like terms: 3r2 + 3r2 = 6r2 -168 + 18r + 6r2 = 3 + 5r + -3r2 + -3 + -5r + 3r2 Reorder the terms: -168 + 18r + 6r2 = 3 + -3 + 5r + -5r + -3r2 + 3r2 Combine like terms: 3 + -3 = 0 -168 + 18r + 6r2 = 0 + 5r + -5r + -3r2 + 3r2 -168 + 18r + 6r2 = 5r + -5r + -3r2 + 3r2 Combine like terms: 5r + -5r = 0 -168 + 18r + 6r2 = 0 + -3r2 + 3r2 -168 + 18r + 6r2 = -3r2 + 3r2 Combine like terms: -3r2 + 3r2 = 0 -168 + 18r + 6r2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-28 + 3r + r2) = 0 Factor a trinomial. 6((-7 + -1r)(4 + -1r)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-7 + -1r)' equal to zero and attempt to solve: Simplifying -7 + -1r = 0 Solving -7 + -1r = 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 + -1r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1r = 0 + 7 -1r = 0 + 7 Combine like terms: 0 + 7 = 7 -1r = 7 Divide each side by '-1'. r = -7 Simplifying r = -7Subproblem 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 = 4Solution
r = {-7, 4}
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