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Simplifying (1 + bx)(1 + 6ax) = 1 + 20x + 171x2 Multiply (1 + bx) * (1 + 6ax) (1(1 + 6ax) + bx(1 + 6ax)) = 1 + 20x + 171x2 ((1 * 1 + 6ax * 1) + bx(1 + 6ax)) = 1 + 20x + 171x2 ((1 + 6ax) + bx(1 + 6ax)) = 1 + 20x + 171x2 (1 + 6ax + (1 * bx + 6ax * bx)) = 1 + 20x + 171x2 Reorder the terms: (1 + 6ax + (6abx2 + 1bx)) = 1 + 20x + 171x2 (1 + 6ax + (6abx2 + 1bx)) = 1 + 20x + 171x2 Reorder the terms: (1 + 6abx2 + 6ax + 1bx) = 1 + 20x + 171x2 (1 + 6abx2 + 6ax + 1bx) = 1 + 20x + 171x2 Add '-1' to each side of the equation. 1 + 6abx2 + 6ax + -1 + 1bx = 1 + 20x + -1 + 171x2 Reorder the terms: 1 + -1 + 6abx2 + 6ax + 1bx = 1 + 20x + -1 + 171x2 Combine like terms: 1 + -1 = 0 0 + 6abx2 + 6ax + 1bx = 1 + 20x + -1 + 171x2 6abx2 + 6ax + 1bx = 1 + 20x + -1 + 171x2 Reorder the terms: 6abx2 + 6ax + 1bx = 1 + -1 + 20x + 171x2 Combine like terms: 1 + -1 = 0 6abx2 + 6ax + 1bx = 0 + 20x + 171x2 6abx2 + 6ax + 1bx = 20x + 171x2 Solving 6abx2 + 6ax + 1bx = 20x + 171x2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bx' to each side of the equation. 6abx2 + 6ax + 1bx + -1bx = 20x + -1bx + 171x2 Combine like terms: 1bx + -1bx = 0 6abx2 + 6ax + 0 = 20x + -1bx + 171x2 6abx2 + 6ax = 20x + -1bx + 171x2 Reorder the terms: 6abx2 + 6ax = -1bx + 20x + 171x2 Reorder the terms: 6abx2 + 6ax + bx + -20x + -171x2 = -1bx + bx + 20x + -20x + 171x2 + -171x2 Combine like terms: -1bx + bx = 0 6abx2 + 6ax + bx + -20x + -171x2 = 0 + 20x + -20x + 171x2 + -171x2 6abx2 + 6ax + bx + -20x + -171x2 = 20x + -20x + 171x2 + -171x2 Combine like terms: 20x + -20x = 0 6abx2 + 6ax + bx + -20x + -171x2 = 0 + 171x2 + -171x2 6abx2 + 6ax + bx + -20x + -171x2 = 171x2 + -171x2 Combine like terms: 171x2 + -171x2 = 0 6abx2 + 6ax + bx + -20x + -171x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(6abx + 6a + b + -20 + -171x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(6abx + 6a + b + -20 + -171x)' equal to zero and attempt to solve: Simplifying 6abx + 6a + b + -20 + -171x = 0 Reorder the terms: -20 + 6a + 6abx + b + -171x = 0 Solving -20 + 6a + 6abx + b + -171x = 0 Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 6a + 6abx + b + 20 + -171x = 0 + 20 Reorder the terms: -20 + 20 + 6a + 6abx + b + -171x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 6a + 6abx + b + -171x = 0 + 20 6a + 6abx + b + -171x = 0 + 20 Combine like terms: 0 + 20 = 20 6a + 6abx + b + -171x = 20 Add '-1b' to each side of the equation. 6a + 6abx + b + -1b + -171x = 20 + -1b Combine like terms: b + -1b = 0 6a + 6abx + 0 + -171x = 20 + -1b 6a + 6abx + -171x = 20 + -1b Add '171x' to each side of the equation. 6a + 6abx + -171x + 171x = 20 + -1b + 171x Combine like terms: -171x + 171x = 0 6a + 6abx + 0 = 20 + -1b + 171x 6a + 6abx = 20 + -1b + 171x 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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