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Simplifying (r + -4)(r + 1) + (r + -4)(r + 6) = 0 Reorder the terms: (-4 + r)(r + 1) + (r + -4)(r + 6) = 0 Reorder the terms: (-4 + r)(1 + r) + (r + -4)(r + 6) = 0 Multiply (-4 + r) * (1 + r) (-4(1 + r) + r(1 + r)) + (r + -4)(r + 6) = 0 ((1 * -4 + r * -4) + r(1 + r)) + (r + -4)(r + 6) = 0 ((-4 + -4r) + r(1 + r)) + (r + -4)(r + 6) = 0 (-4 + -4r + (1 * r + r * r)) + (r + -4)(r + 6) = 0 (-4 + -4r + (1r + r2)) + (r + -4)(r + 6) = 0 Combine like terms: -4r + 1r = -3r (-4 + -3r + r2) + (r + -4)(r + 6) = 0 Reorder the terms: -4 + -3r + r2 + (-4 + r)(r + 6) = 0 Reorder the terms: -4 + -3r + r2 + (-4 + r)(6 + r) = 0 Multiply (-4 + r) * (6 + r) -4 + -3r + r2 + (-4(6 + r) + r(6 + r)) = 0 -4 + -3r + r2 + ((6 * -4 + r * -4) + r(6 + r)) = 0 -4 + -3r + r2 + ((-24 + -4r) + r(6 + r)) = 0 -4 + -3r + r2 + (-24 + -4r + (6 * r + r * r)) = 0 -4 + -3r + r2 + (-24 + -4r + (6r + r2)) = 0 Combine like terms: -4r + 6r = 2r -4 + -3r + r2 + (-24 + 2r + r2) = 0 Reorder the terms: -4 + -24 + -3r + 2r + r2 + r2 = 0 Combine like terms: -4 + -24 = -28 -28 + -3r + 2r + r2 + r2 = 0 Combine like terms: -3r + 2r = -1r -28 + -1r + r2 + r2 = 0 Combine like terms: r2 + r2 = 2r2 -28 + -1r + 2r2 = 0 Solving -28 + -1r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (-7 + -2r)(4 + -1r) = 0Subproblem 1
Set the factor '(-7 + -2r)' equal to zero and attempt to solve: Simplifying -7 + -2r = 0 Solving -7 + -2r = 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 + -2r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2r = 0 + 7 -2r = 0 + 7 Combine like terms: 0 + 7 = 7 -2r = 7 Divide each side by '-2'. r = -3.5 Simplifying r = -3.5Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve: Simplifying 4 + -1r = 0 Solving 4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1r = 0 + -4 -1r = 0 + -4 Combine like terms: 0 + -4 = -4 -1r = -4 Divide each side by '-1'. r = 4 Simplifying r = 4Solution
r = {-3.5, 4}
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