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Simplifying (r + -5)(r + -7) = 0 Reorder the terms: (-5 + r)(r + -7) = 0 Reorder the terms: (-5 + r)(-7 + r) = 0 Multiply (-5 + r) * (-7 + r) (-5(-7 + r) + r(-7 + r)) = 0 ((-7 * -5 + r * -5) + r(-7 + r)) = 0 ((35 + -5r) + r(-7 + r)) = 0 (35 + -5r + (-7 * r + r * r)) = 0 (35 + -5r + (-7r + r2)) = 0 Combine like terms: -5r + -7r = -12r (35 + -12r + r2) = 0 Solving 35 + -12r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (5 + -1r)(7 + -1r) = 0Subproblem 1
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 = 5Subproblem 2
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 = 7Solution
r = {5, 7}
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