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Simplifying r2 + 10r + -75 = 0 Reorder the terms: -75 + 10r + r2 = 0 Solving -75 + 10r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (-15 + -1r)(5 + -1r) = 0Subproblem 1
Set the factor '(-15 + -1r)' equal to zero and attempt to solve: Simplifying -15 + -1r = 0 Solving -15 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1r = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1r = 0 + 15 -1r = 0 + 15 Combine like terms: 0 + 15 = 15 -1r = 15 Divide each side by '-1'. r = -15 Simplifying r = -15Subproblem 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 = {-15, 5}
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