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Simplifying (R2 + 6r + 5)(5r2 + r + -5) = 0 Reorder the terms: (5 + R2 + 6r)(5r2 + r + -5) = 0 Reorder the terms: (5 + R2 + 6r)(-5 + r + 5r2) = 0 Multiply (5 + R2 + 6r) * (-5 + r + 5r2) (5(-5 + r + 5r2) + R2(-5 + r + 5r2) + 6r * (-5 + r + 5r2)) = 0 ((-5 * 5 + r * 5 + 5r2 * 5) + R2(-5 + r + 5r2) + 6r * (-5 + r + 5r2)) = 0 ((-25 + 5r + 25r2) + R2(-5 + r + 5r2) + 6r * (-5 + r + 5r2)) = 0 (-25 + 5r + 25r2 + (-5 * R2 + r * R2 + 5r2 * R2) + 6r * (-5 + r + 5r2)) = 0 (-25 + 5r + 25r2 + (-5R2 + rR2 + 5r2R2) + 6r * (-5 + r + 5r2)) = 0 (-25 + 5r + 25r2 + -5R2 + rR2 + 5r2R2 + (-5 * 6r + r * 6r + 5r2 * 6r)) = 0 (-25 + 5r + 25r2 + -5R2 + rR2 + 5r2R2 + (-30r + 6r2 + 30r3)) = 0 Reorder the terms: (-25 + -5R2 + 5r + -30r + rR2 + 25r2 + 6r2 + 5r2R2 + 30r3) = 0 Combine like terms: 5r + -30r = -25r (-25 + -5R2 + -25r + rR2 + 25r2 + 6r2 + 5r2R2 + 30r3) = 0 Combine like terms: 25r2 + 6r2 = 31r2 (-25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3) = 0 Solving -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 0 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '25' to each side of the equation. -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 25 + 30r3 = 0 + 25 Reorder the terms: -25 + 25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 0 + 25 -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 0 + 25 Combine like terms: 0 + 25 = 25 -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 25 Add '25r' to each side of the equation. -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 25r + 30r3 = 25 + 25r Reorder the terms: -5R2 + -25r + 25r + rR2 + 31r2 + 5r2R2 + 30r3 = 25 + 25r Combine like terms: -25r + 25r = 0 -5R2 + 0 + rR2 + 31r2 + 5r2R2 + 30r3 = 25 + 25r -5R2 + rR2 + 31r2 + 5r2R2 + 30r3 = 25 + 25r Add '-31r2' to each side of the equation. -5R2 + rR2 + 31r2 + 5r2R2 + -31r2 + 30r3 = 25 + 25r + -31r2 Reorder the terms: -5R2 + rR2 + 31r2 + -31r2 + 5r2R2 + 30r3 = 25 + 25r + -31r2 Combine like terms: 31r2 + -31r2 = 0 -5R2 + rR2 + 0 + 5r2R2 + 30r3 = 25 + 25r + -31r2 -5R2 + rR2 + 5r2R2 + 30r3 = 25 + 25r + -31r2 Add '-30r3' to each side of the equation. -5R2 + rR2 + 5r2R2 + 30r3 + -30r3 = 25 + 25r + -31r2 + -30r3 Combine like terms: 30r3 + -30r3 = 0 -5R2 + rR2 + 5r2R2 + 0 = 25 + 25r + -31r2 + -30r3 -5R2 + rR2 + 5r2R2 = 25 + 25r + -31r2 + -30r3 Reorder the terms: -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 25 + 25r + -31r2 + -30r3 + -25 + -25r + 31r2 + 30r3 Reorder the terms: -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 25 + -25 + 25r + -25r + -31r2 + 31r2 + -30r3 + 30r3 Combine like terms: 25 + -25 = 0 -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 0 + 25r + -25r + -31r2 + 31r2 + -30r3 + 30r3 -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 25r + -25r + -31r2 + 31r2 + -30r3 + 30r3 Combine like terms: 25r + -25r = 0 -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 0 + -31r2 + 31r2 + -30r3 + 30r3 -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = -31r2 + 31r2 + -30r3 + 30r3 Combine like terms: -31r2 + 31r2 = 0 -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 0 + -30r3 + 30r3 -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = -30r3 + 30r3 Combine like terms: -30r3 + 30r3 = 0 -25 + -5R2 + -25r + rR2 + 31r2 + 5r2R2 + 30r3 = 0 The solution to this equation could not be determined.
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