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Simplifying (8r + 1)(3r + -5) = 0 Reorder the terms: (1 + 8r)(3r + -5) = 0 Reorder the terms: (1 + 8r)(-5 + 3r) = 0 Multiply (1 + 8r) * (-5 + 3r) (1(-5 + 3r) + 8r * (-5 + 3r)) = 0 ((-5 * 1 + 3r * 1) + 8r * (-5 + 3r)) = 0 ((-5 + 3r) + 8r * (-5 + 3r)) = 0 (-5 + 3r + (-5 * 8r + 3r * 8r)) = 0 (-5 + 3r + (-40r + 24r2)) = 0 Combine like terms: 3r + -40r = -37r (-5 + -37r + 24r2) = 0 Solving -5 + -37r + 24r2 = 0 Solving for variable 'r'. Factor a trinomial. (-1 + -8r)(5 + -3r) = 0Subproblem 1
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 = -0.125Subproblem 2
Set the factor '(5 + -3r)' equal to zero and attempt to solve: Simplifying 5 + -3r = 0 Solving 5 + -3r = 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 + -3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3r = 0 + -5 -3r = 0 + -5 Combine like terms: 0 + -5 = -5 -3r = -5 Divide each side by '-3'. r = 1.666666667 Simplifying r = 1.666666667Solution
r = {-0.125, 1.666666667}
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