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Simplifying (r + -2)(r + -7) = 0 Reorder the terms: (-2 + r)(r + -7) = 0 Reorder the terms: (-2 + r)(-7 + r) = 0 Multiply (-2 + r) * (-7 + r) (-2(-7 + r) + r(-7 + r)) = 0 ((-7 * -2 + r * -2) + r(-7 + r)) = 0 ((14 + -2r) + r(-7 + r)) = 0 (14 + -2r + (-7 * r + r * r)) = 0 (14 + -2r + (-7r + r2)) = 0 Combine like terms: -2r + -7r = -9r (14 + -9r + r2) = 0 Solving 14 + -9r + 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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