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Simplifying 6r2 + 7r = -1r + 90 + 4r2 Reorder the terms: 7r + 6r2 = -1r + 90 + 4r2 Reorder the terms: 7r + 6r2 = 90 + -1r + 4r2 Solving 7r + 6r2 = 90 + -1r + 4r2 Solving for variable 'r'. Reorder the terms: -90 + 7r + r + 6r2 + -4r2 = 90 + -1r + 4r2 + -90 + r + -4r2 Combine like terms: 7r + r = 8r -90 + 8r + 6r2 + -4r2 = 90 + -1r + 4r2 + -90 + r + -4r2 Combine like terms: 6r2 + -4r2 = 2r2 -90 + 8r + 2r2 = 90 + -1r + 4r2 + -90 + r + -4r2 Reorder the terms: -90 + 8r + 2r2 = 90 + -90 + -1r + r + 4r2 + -4r2 Combine like terms: 90 + -90 = 0 -90 + 8r + 2r2 = 0 + -1r + r + 4r2 + -4r2 -90 + 8r + 2r2 = -1r + r + 4r2 + -4r2 Combine like terms: -1r + r = 0 -90 + 8r + 2r2 = 0 + 4r2 + -4r2 -90 + 8r + 2r2 = 4r2 + -4r2 Combine like terms: 4r2 + -4r2 = 0 -90 + 8r + 2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + 4r + r2) = 0 Factor a trinomial. 2((-9 + -1r)(5 + -1r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -1r)' equal to zero and attempt to solve: Simplifying -9 + -1r = 0 Solving -9 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1r = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1r = 0 + 9 -1r = 0 + 9 Combine like terms: 0 + 9 = 9 -1r = 9 Divide each side by '-1'. r = -9 Simplifying r = -9Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 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 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5Solution
r = {-9, 5}
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