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Simplifying (1 + -1ax)(2x + 1) = 0 Reorder the terms: (1 + -1ax)(1 + 2x) = 0 Multiply (1 + -1ax) * (1 + 2x) (1(1 + 2x) + -1ax * (1 + 2x)) = 0 ((1 * 1 + 2x * 1) + -1ax * (1 + 2x)) = 0 ((1 + 2x) + -1ax * (1 + 2x)) = 0 (1 + 2x + (1 * -1ax + 2x * -1ax)) = 0 (1 + 2x + (-1ax + -2ax2)) = 0 Reorder the terms: (1 + -1ax + -2ax2 + 2x) = 0 (1 + -1ax + -2ax2 + 2x) = 0 Solving 1 + -1ax + -2ax2 + 2x = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1ax + -2ax2 + -1 + 2x = 0 + -1 Reorder the terms: 1 + -1 + -1ax + -2ax2 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1ax + -2ax2 + 2x = 0 + -1 -1ax + -2ax2 + 2x = 0 + -1 Combine like terms: 0 + -1 = -1 -1ax + -2ax2 + 2x = -1 Add '-2x' to each side of the equation. -1ax + -2ax2 + 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 -1ax + -2ax2 + 0 = -1 + -2x -1ax + -2ax2 = -1 + -2x Reorder the terms: 1 + -1ax + -2ax2 + 2x = -1 + -2x + 1 + 2x Reorder the terms: 1 + -1ax + -2ax2 + 2x = -1 + 1 + -2x + 2x Combine like terms: -1 + 1 = 0 1 + -1ax + -2ax2 + 2x = 0 + -2x + 2x 1 + -1ax + -2ax2 + 2x = -2x + 2x Combine like terms: -2x + 2x = 0 1 + -1ax + -2ax2 + 2x = 0 The solution to this equation could not be determined.
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