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Simplifying 5r2 + 5r + -23 = 7 Reorder the terms: -23 + 5r + 5r2 = 7 Solving -23 + 5r + 5r2 = 7 Solving for variable 'r'. Reorder the terms: -23 + -7 + 5r + 5r2 = 7 + -7 Combine like terms: -23 + -7 = -30 -30 + 5r + 5r2 = 7 + -7 Combine like terms: 7 + -7 = 0 -30 + 5r + 5r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + r + r2) = 0 Factor a trinomial. 5((-3 + -1r)(2 + -1r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve: Simplifying -3 + -1r = 0 Solving -3 + -1r = 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 + -1r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1r = 0 + 3 -1r = 0 + 3 Combine like terms: 0 + 3 = 3 -1r = 3 Divide each side by '-1'. r = -3 Simplifying r = -3Subproblem 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 = 2Solution
r = {-3, 2}
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