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Simplifying (7r + -5)(r + 8) = 0 Reorder the terms: (-5 + 7r)(r + 8) = 0 Reorder the terms: (-5 + 7r)(8 + r) = 0 Multiply (-5 + 7r) * (8 + r) (-5(8 + r) + 7r * (8 + r)) = 0 ((8 * -5 + r * -5) + 7r * (8 + r)) = 0 ((-40 + -5r) + 7r * (8 + r)) = 0 (-40 + -5r + (8 * 7r + r * 7r)) = 0 (-40 + -5r + (56r + 7r2)) = 0 Combine like terms: -5r + 56r = 51r (-40 + 51r + 7r2) = 0 Solving -40 + 51r + 7r2 = 0 Solving for variable 'r'. Factor a trinomial. (-8 + -1r)(5 + -7r) = 0Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve: Simplifying -8 + -1r = 0 Solving -8 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1r = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1r = 0 + 8 -1r = 0 + 8 Combine like terms: 0 + 8 = 8 -1r = 8 Divide each side by '-1'. r = -8 Simplifying r = -8Subproblem 2
Set the factor '(5 + -7r)' equal to zero and attempt to solve: Simplifying 5 + -7r = 0 Solving 5 + -7r = 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 + -7r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7r = 0 + -5 -7r = 0 + -5 Combine like terms: 0 + -5 = -5 -7r = -5 Divide each side by '-7'. r = 0.7142857143 Simplifying r = 0.7142857143Solution
r = {-8, 0.7142857143}
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