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Simplifying (8r + -4)(r + 7) + -1(3r + -1)(r + 7) = 0 Reorder the terms: (-4 + 8r)(r + 7) + -1(3r + -1)(r + 7) = 0 Reorder the terms: (-4 + 8r)(7 + r) + -1(3r + -1)(r + 7) = 0 Multiply (-4 + 8r) * (7 + r) (-4(7 + r) + 8r * (7 + r)) + -1(3r + -1)(r + 7) = 0 ((7 * -4 + r * -4) + 8r * (7 + r)) + -1(3r + -1)(r + 7) = 0 ((-28 + -4r) + 8r * (7 + r)) + -1(3r + -1)(r + 7) = 0 (-28 + -4r + (7 * 8r + r * 8r)) + -1(3r + -1)(r + 7) = 0 (-28 + -4r + (56r + 8r2)) + -1(3r + -1)(r + 7) = 0 Combine like terms: -4r + 56r = 52r (-28 + 52r + 8r2) + -1(3r + -1)(r + 7) = 0 Reorder the terms: -28 + 52r + 8r2 + -1(-1 + 3r)(r + 7) = 0 Reorder the terms: -28 + 52r + 8r2 + -1(-1 + 3r)(7 + r) = 0 Multiply (-1 + 3r) * (7 + r) -28 + 52r + 8r2 + -1(-1(7 + r) + 3r * (7 + r)) = 0 -28 + 52r + 8r2 + -1((7 * -1 + r * -1) + 3r * (7 + r)) = 0 -28 + 52r + 8r2 + -1((-7 + -1r) + 3r * (7 + r)) = 0 -28 + 52r + 8r2 + -1(-7 + -1r + (7 * 3r + r * 3r)) = 0 -28 + 52r + 8r2 + -1(-7 + -1r + (21r + 3r2)) = 0 Combine like terms: -1r + 21r = 20r -28 + 52r + 8r2 + -1(-7 + 20r + 3r2) = 0 -28 + 52r + 8r2 + (-7 * -1 + 20r * -1 + 3r2 * -1) = 0 -28 + 52r + 8r2 + (7 + -20r + -3r2) = 0 Reorder the terms: -28 + 7 + 52r + -20r + 8r2 + -3r2 = 0 Combine like terms: -28 + 7 = -21 -21 + 52r + -20r + 8r2 + -3r2 = 0 Combine like terms: 52r + -20r = 32r -21 + 32r + 8r2 + -3r2 = 0 Combine like terms: 8r2 + -3r2 = 5r2 -21 + 32r + 5r2 = 0 Solving -21 + 32r + 5r2 = 0 Solving for variable 'r'. Factor a trinomial. (-7 + -1r)(3 + -5r) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(3 + -5r)' equal to zero and attempt to solve: Simplifying 3 + -5r = 0 Solving 3 + -5r = 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 + -5r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5r = 0 + -3 -5r = 0 + -3 Combine like terms: 0 + -3 = -3 -5r = -3 Divide each side by '-5'. r = 0.6 Simplifying r = 0.6Solution
r = {-7, 0.6}
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