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Simplifying (8r + -1)(5r + 7) = 0 Reorder the terms: (-1 + 8r)(5r + 7) = 0 Reorder the terms: (-1 + 8r)(7 + 5r) = 0 Multiply (-1 + 8r) * (7 + 5r) (-1(7 + 5r) + 8r * (7 + 5r)) = 0 ((7 * -1 + 5r * -1) + 8r * (7 + 5r)) = 0 ((-7 + -5r) + 8r * (7 + 5r)) = 0 (-7 + -5r + (7 * 8r + 5r * 8r)) = 0 (-7 + -5r + (56r + 40r2)) = 0 Combine like terms: -5r + 56r = 51r (-7 + 51r + 40r2) = 0 Solving -7 + 51r + 40r2 = 0 Solving for variable 'r'. Factor a trinomial. (-7 + -5r)(1 + -8r) = 0Subproblem 1
Set the factor '(-7 + -5r)' equal to zero and attempt to solve: Simplifying -7 + -5r = 0 Solving -7 + -5r = 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 + -5r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5r = 0 + 7 -5r = 0 + 7 Combine like terms: 0 + 7 = 7 -5r = 7 Divide each side by '-5'. r = -1.4 Simplifying r = -1.4Subproblem 2
Set the factor '(1 + -8r)' equal to zero and attempt to solve: Simplifying 1 + -8r = 0 Solving 1 + -8r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -8r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8r = 0 + -1 -8r = 0 + -1 Combine like terms: 0 + -1 = -1 -8r = -1 Divide each side by '-8'. r = 0.125 Simplifying r = 0.125Solution
r = {-1.4, 0.125}
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