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Simplifying (8r + -7)(4r + -3) = 0 Reorder the terms: (-7 + 8r)(4r + -3) = 0 Reorder the terms: (-7 + 8r)(-3 + 4r) = 0 Multiply (-7 + 8r) * (-3 + 4r) (-7(-3 + 4r) + 8r * (-3 + 4r)) = 0 ((-3 * -7 + 4r * -7) + 8r * (-3 + 4r)) = 0 ((21 + -28r) + 8r * (-3 + 4r)) = 0 (21 + -28r + (-3 * 8r + 4r * 8r)) = 0 (21 + -28r + (-24r + 32r2)) = 0 Combine like terms: -28r + -24r = -52r (21 + -52r + 32r2) = 0 Solving 21 + -52r + 32r2 = 0 Solving for variable 'r'. Factor a trinomial. (3 + -4r)(7 + -8r) = 0Subproblem 1
Set the factor '(3 + -4r)' equal to zero and attempt to solve: Simplifying 3 + -4r = 0 Solving 3 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4r = 0 + -3 -4r = 0 + -3 Combine like terms: 0 + -3 = -3 -4r = -3 Divide each side by '-4'. r = 0.75 Simplifying r = 0.75Subproblem 2
Set the factor '(7 + -8r)' equal to zero and attempt to solve: Simplifying 7 + -8r = 0 Solving 7 + -8r = 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 + -8r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8r = 0 + -7 -8r = 0 + -7 Combine like terms: 0 + -7 = -7 -8r = -7 Divide each side by '-8'. r = 0.875 Simplifying r = 0.875Solution
r = {0.75, 0.875}
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