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Simplifying (3x + b + 3)(3x + b + 3) = (3x + -1b + 3)(3x + -1b + -3) Reorder the terms: (3 + b + 3x)(3x + b + 3) = (3x + -1b + 3)(3x + -1b + -3) Reorder the terms: (3 + b + 3x)(3 + b + 3x) = (3x + -1b + 3)(3x + -1b + -3) Multiply (3 + b + 3x) * (3 + b + 3x) (3(3 + b + 3x) + b(3 + b + 3x) + 3x * (3 + b + 3x)) = (3x + -1b + 3)(3x + -1b + -3) ((3 * 3 + b * 3 + 3x * 3) + b(3 + b + 3x) + 3x * (3 + b + 3x)) = (3x + -1b + 3)(3x + -1b + -3) ((9 + 3b + 9x) + b(3 + b + 3x) + 3x * (3 + b + 3x)) = (3x + -1b + 3)(3x + -1b + -3) (9 + 3b + 9x + (3 * b + b * b + 3x * b) + 3x * (3 + b + 3x)) = (3x + -1b + 3)(3x + -1b + -3) Reorder the terms: (9 + 3b + 9x + (3b + 3bx + b2) + 3x * (3 + b + 3x)) = (3x + -1b + 3)(3x + -1b + -3) (9 + 3b + 9x + (3b + 3bx + b2) + 3x * (3 + b + 3x)) = (3x + -1b + 3)(3x + -1b + -3) (9 + 3b + 9x + 3b + 3bx + b2 + (3 * 3x + b * 3x + 3x * 3x)) = (3x + -1b + 3)(3x + -1b + -3) Reorder the terms: (9 + 3b + 9x + 3b + 3bx + b2 + (3bx + 9x + 9x2)) = (3x + -1b + 3)(3x + -1b + -3) (9 + 3b + 9x + 3b + 3bx + b2 + (3bx + 9x + 9x2)) = (3x + -1b + 3)(3x + -1b + -3) Reorder the terms: (9 + 3b + 3b + 3bx + 3bx + b2 + 9x + 9x + 9x2) = (3x + -1b + 3)(3x + -1b + -3) Combine like terms: 3b + 3b = 6b (9 + 6b + 3bx + 3bx + b2 + 9x + 9x + 9x2) = (3x + -1b + 3)(3x + -1b + -3) Combine like terms: 3bx + 3bx = 6bx (9 + 6b + 6bx + b2 + 9x + 9x + 9x2) = (3x + -1b + 3)(3x + -1b + -3) Combine like terms: 9x + 9x = 18x (9 + 6b + 6bx + b2 + 18x + 9x2) = (3x + -1b + 3)(3x + -1b + -3) Reorder the terms: 9 + 6b + 6bx + b2 + 18x + 9x2 = (3 + -1b + 3x)(3x + -1b + -3) Reorder the terms: 9 + 6b + 6bx + b2 + 18x + 9x2 = (3 + -1b + 3x)(-3 + -1b + 3x) Multiply (3 + -1b + 3x) * (-3 + -1b + 3x) 9 + 6b + 6bx + b2 + 18x + 9x2 = (3(-3 + -1b + 3x) + -1b * (-3 + -1b + 3x) + 3x * (-3 + -1b + 3x)) 9 + 6b + 6bx + b2 + 18x + 9x2 = ((-3 * 3 + -1b * 3 + 3x * 3) + -1b * (-3 + -1b + 3x) + 3x * (-3 + -1b + 3x)) 9 + 6b + 6bx + b2 + 18x + 9x2 = ((-9 + -3b + 9x) + -1b * (-3 + -1b + 3x) + 3x * (-3 + -1b + 3x)) 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -3b + 9x + (-3 * -1b + -1b * -1b + 3x * -1b) + 3x * (-3 + -1b + 3x)) Reorder the terms: 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -3b + 9x + (3b + -3bx + 1b2) + 3x * (-3 + -1b + 3x)) 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -3b + 9x + (3b + -3bx + 1b2) + 3x * (-3 + -1b + 3x)) 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -3b + 9x + 3b + -3bx + 1b2 + (-3 * 3x + -1b * 3x + 3x * 3x)) Reorder the terms: 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -3b + 9x + 3b + -3bx + 1b2 + (-3bx + -9x + 9x2)) 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -3b + 9x + 3b + -3bx + 1b2 + (-3bx + -9x + 9x2)) Reorder the terms: 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -3b + 3b + -3bx + -3bx + 1b2 + 9x + -9x + 9x2) Combine like terms: -3b + 3b = 0 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + 0 + -3bx + -3bx + 1b2 + 9x + -9x + 9x2) 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -3bx + -3bx + 1b2 + 9x + -9x + 9x2) Combine like terms: -3bx + -3bx = -6bx 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -6bx + 1b2 + 9x + -9x + 9x2) Combine like terms: 9x + -9x = 0 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -6bx + 1b2 + 0 + 9x2) 9 + 6b + 6bx + b2 + 18x + 9x2 = (-9 + -6bx + 1b2 + 9x2) Add '-9x2' to each side of the equation. 9 + 6b + 6bx + b2 + 18x + 9x2 + -9x2 = -9 + -6bx + 1b2 + 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 9 + 6b + 6bx + b2 + 18x + 0 = -9 + -6bx + 1b2 + 9x2 + -9x2 9 + 6b + 6bx + b2 + 18x = -9 + -6bx + 1b2 + 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 9 + 6b + 6bx + b2 + 18x = -9 + -6bx + 1b2 + 0 9 + 6b + 6bx + b2 + 18x = -9 + -6bx + 1b2 Solving 9 + 6b + 6bx + b2 + 18x = -9 + -6bx + 1b2 Solving for variable 'b'. Reorder the terms: 9 + 9 + 6b + 6bx + 6bx + b2 + -1b2 + 18x = -9 + -6bx + 1b2 + 9 + 6bx + -1b2 Combine like terms: 9 + 9 = 18 18 + 6b + 6bx + 6bx + b2 + -1b2 + 18x = -9 + -6bx + 1b2 + 9 + 6bx + -1b2 Combine like terms: 6bx + 6bx = 12bx 18 + 6b + 12bx + b2 + -1b2 + 18x = -9 + -6bx + 1b2 + 9 + 6bx + -1b2 Combine like terms: b2 + -1b2 = 0 18 + 6b + 12bx + 0 + 18x = -9 + -6bx + 1b2 + 9 + 6bx + -1b2 18 + 6b + 12bx + 18x = -9 + -6bx + 1b2 + 9 + 6bx + -1b2 Reorder the terms: 18 + 6b + 12bx + 18x = -9 + 9 + -6bx + 6bx + 1b2 + -1b2 Combine like terms: -9 + 9 = 0 18 + 6b + 12bx + 18x = 0 + -6bx + 6bx + 1b2 + -1b2 18 + 6b + 12bx + 18x = -6bx + 6bx + 1b2 + -1b2 Combine like terms: -6bx + 6bx = 0 18 + 6b + 12bx + 18x = 0 + 1b2 + -1b2 18 + 6b + 12bx + 18x = 1b2 + -1b2 Combine like terms: 1b2 + -1b2 = 0 18 + 6b + 12bx + 18x = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(3 + b + 2bx + 3x) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + b + 2bx + 3x)' equal to zero and attempt to solve: Simplifying 3 + b + 2bx + 3x = 0 Solving 3 + b + 2bx + 3x = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + b + 2bx + -3 + 3x = 0 + -3 Reorder the terms: 3 + -3 + b + 2bx + 3x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + b + 2bx + 3x = 0 + -3 b + 2bx + 3x = 0 + -3 Combine like terms: 0 + -3 = -3 b + 2bx + 3x = -3 Add '-3x' to each side of the equation. b + 2bx + 3x + -3x = -3 + -3x Combine like terms: 3x + -3x = 0 b + 2bx + 0 = -3 + -3x b + 2bx = -3 + -3x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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