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Simplifying (1 + -4x)(1 + -3x) = 6x(2x + -1) Multiply (1 + -4x) * (1 + -3x) (1(1 + -3x) + -4x * (1 + -3x)) = 6x(2x + -1) ((1 * 1 + -3x * 1) + -4x * (1 + -3x)) = 6x(2x + -1) ((1 + -3x) + -4x * (1 + -3x)) = 6x(2x + -1) (1 + -3x + (1 * -4x + -3x * -4x)) = 6x(2x + -1) (1 + -3x + (-4x + 12x2)) = 6x(2x + -1) Combine like terms: -3x + -4x = -7x (1 + -7x + 12x2) = 6x(2x + -1) Reorder the terms: 1 + -7x + 12x2 = 6x(-1 + 2x) 1 + -7x + 12x2 = (-1 * 6x + 2x * 6x) 1 + -7x + 12x2 = (-6x + 12x2) Add '-12x2' to each side of the equation. 1 + -7x + 12x2 + -12x2 = -6x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 1 + -7x + 0 = -6x + 12x2 + -12x2 1 + -7x = -6x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 1 + -7x = -6x + 0 1 + -7x = -6x Solving 1 + -7x = -6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6x' to each side of the equation. 1 + -7x + 6x = -6x + 6x Combine like terms: -7x + 6x = -1x 1 + -1x = -6x + 6x Combine like terms: -6x + 6x = 0 1 + -1x = 0 Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1
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