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Simplifying (r + -4)(r + 7) + (r + -4)(r + 2) = 0 Reorder the terms: (-4 + r)(r + 7) + (r + -4)(r + 2) = 0 Reorder the terms: (-4 + r)(7 + r) + (r + -4)(r + 2) = 0 Multiply (-4 + r) * (7 + r) (-4(7 + r) + r(7 + r)) + (r + -4)(r + 2) = 0 ((7 * -4 + r * -4) + r(7 + r)) + (r + -4)(r + 2) = 0 ((-28 + -4r) + r(7 + r)) + (r + -4)(r + 2) = 0 (-28 + -4r + (7 * r + r * r)) + (r + -4)(r + 2) = 0 (-28 + -4r + (7r + r2)) + (r + -4)(r + 2) = 0 Combine like terms: -4r + 7r = 3r (-28 + 3r + r2) + (r + -4)(r + 2) = 0 Reorder the terms: -28 + 3r + r2 + (-4 + r)(r + 2) = 0 Reorder the terms: -28 + 3r + r2 + (-4 + r)(2 + r) = 0 Multiply (-4 + r) * (2 + r) -28 + 3r + r2 + (-4(2 + r) + r(2 + r)) = 0 -28 + 3r + r2 + ((2 * -4 + r * -4) + r(2 + r)) = 0 -28 + 3r + r2 + ((-8 + -4r) + r(2 + r)) = 0 -28 + 3r + r2 + (-8 + -4r + (2 * r + r * r)) = 0 -28 + 3r + r2 + (-8 + -4r + (2r + r2)) = 0 Combine like terms: -4r + 2r = -2r -28 + 3r + r2 + (-8 + -2r + r2) = 0 Reorder the terms: -28 + -8 + 3r + -2r + r2 + r2 = 0 Combine like terms: -28 + -8 = -36 -36 + 3r + -2r + r2 + r2 = 0 Combine like terms: 3r + -2r = 1r -36 + 1r + r2 + r2 = 0 Combine like terms: r2 + r2 = 2r2 -36 + 1r + 2r2 = 0 Solving -36 + 1r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (-9 + -2r)(4 + -1r) = 0Subproblem 1
Set the factor '(-9 + -2r)' equal to zero and attempt to solve: Simplifying -9 + -2r = 0 Solving -9 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2r = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2r = 0 + 9 -2r = 0 + 9 Combine like terms: 0 + 9 = 9 -2r = 9 Divide each side by '-2'. r = -4.5 Simplifying r = -4.5Subproblem 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 = {-4.5, 4}
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