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Simplifying (2r + 5)(r + -6) = (2r + 3)(r + -4) Reorder the terms: (5 + 2r)(r + -6) = (2r + 3)(r + -4) Reorder the terms: (5 + 2r)(-6 + r) = (2r + 3)(r + -4) Multiply (5 + 2r) * (-6 + r) (5(-6 + r) + 2r * (-6 + r)) = (2r + 3)(r + -4) ((-6 * 5 + r * 5) + 2r * (-6 + r)) = (2r + 3)(r + -4) ((-30 + 5r) + 2r * (-6 + r)) = (2r + 3)(r + -4) (-30 + 5r + (-6 * 2r + r * 2r)) = (2r + 3)(r + -4) (-30 + 5r + (-12r + 2r2)) = (2r + 3)(r + -4) Combine like terms: 5r + -12r = -7r (-30 + -7r + 2r2) = (2r + 3)(r + -4) Reorder the terms: -30 + -7r + 2r2 = (3 + 2r)(r + -4) Reorder the terms: -30 + -7r + 2r2 = (3 + 2r)(-4 + r) Multiply (3 + 2r) * (-4 + r) -30 + -7r + 2r2 = (3(-4 + r) + 2r * (-4 + r)) -30 + -7r + 2r2 = ((-4 * 3 + r * 3) + 2r * (-4 + r)) -30 + -7r + 2r2 = ((-12 + 3r) + 2r * (-4 + r)) -30 + -7r + 2r2 = (-12 + 3r + (-4 * 2r + r * 2r)) -30 + -7r + 2r2 = (-12 + 3r + (-8r + 2r2)) Combine like terms: 3r + -8r = -5r -30 + -7r + 2r2 = (-12 + -5r + 2r2) Add '-2r2' to each side of the equation. -30 + -7r + 2r2 + -2r2 = -12 + -5r + 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 -30 + -7r + 0 = -12 + -5r + 2r2 + -2r2 -30 + -7r = -12 + -5r + 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 -30 + -7r = -12 + -5r + 0 -30 + -7r = -12 + -5r Solving -30 + -7r = -12 + -5r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5r' to each side of the equation. -30 + -7r + 5r = -12 + -5r + 5r Combine like terms: -7r + 5r = -2r -30 + -2r = -12 + -5r + 5r Combine like terms: -5r + 5r = 0 -30 + -2r = -12 + 0 -30 + -2r = -12 Add '30' to each side of the equation. -30 + 30 + -2r = -12 + 30 Combine like terms: -30 + 30 = 0 0 + -2r = -12 + 30 -2r = -12 + 30 Combine like terms: -12 + 30 = 18 -2r = 18 Divide each side by '-2'. r = -9 Simplifying r = -9
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