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Simplifying 3r2 + 18r + 81 = 102 Reorder the terms: 81 + 18r + 3r2 = 102 Solving 81 + 18r + 3r2 = 102 Solving for variable 'r'. Reorder the terms: 81 + -102 + 18r + 3r2 = 102 + -102 Combine like terms: 81 + -102 = -21 -21 + 18r + 3r2 = 102 + -102 Combine like terms: 102 + -102 = 0 -21 + 18r + 3r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 6r + r2) = 0 Factor a trinomial. 3((-7 + -1r)(1 + -1r)) = 0 Ignore the factor 3.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 '(1 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1Solution
r = {-7, 1}
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