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Simplifying (r + -7)(r + 2) = 0 Reorder the terms: (-7 + r)(r + 2) = 0 Reorder the terms: (-7 + r)(2 + r) = 0 Multiply (-7 + r) * (2 + r) (-7(2 + r) + r(2 + r)) = 0 ((2 * -7 + r * -7) + r(2 + r)) = 0 ((-14 + -7r) + r(2 + r)) = 0 (-14 + -7r + (2 * r + r * r)) = 0 (-14 + -7r + (2r + r2)) = 0 Combine like terms: -7r + 2r = -5r (-14 + -5r + r2) = 0 Solving -14 + -5r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (-2 + -1r)(7 + -1r) = 0Subproblem 1
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 = -2Subproblem 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 = {-2, 7}
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