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Simplifying (12x + -5)(4x + -1) + (3x + -7)(1 + -16x) = 81 Reorder the terms: (-5 + 12x)(4x + -1) + (3x + -7)(1 + -16x) = 81 Reorder the terms: (-5 + 12x)(-1 + 4x) + (3x + -7)(1 + -16x) = 81 Multiply (-5 + 12x) * (-1 + 4x) (-5(-1 + 4x) + 12x * (-1 + 4x)) + (3x + -7)(1 + -16x) = 81 ((-1 * -5 + 4x * -5) + 12x * (-1 + 4x)) + (3x + -7)(1 + -16x) = 81 ((5 + -20x) + 12x * (-1 + 4x)) + (3x + -7)(1 + -16x) = 81 (5 + -20x + (-1 * 12x + 4x * 12x)) + (3x + -7)(1 + -16x) = 81 (5 + -20x + (-12x + 48x2)) + (3x + -7)(1 + -16x) = 81 Combine like terms: -20x + -12x = -32x (5 + -32x + 48x2) + (3x + -7)(1 + -16x) = 81 Reorder the terms: 5 + -32x + 48x2 + (-7 + 3x)(1 + -16x) = 81 Multiply (-7 + 3x) * (1 + -16x) 5 + -32x + 48x2 + (-7(1 + -16x) + 3x * (1 + -16x)) = 81 5 + -32x + 48x2 + ((1 * -7 + -16x * -7) + 3x * (1 + -16x)) = 81 5 + -32x + 48x2 + ((-7 + 112x) + 3x * (1 + -16x)) = 81 5 + -32x + 48x2 + (-7 + 112x + (1 * 3x + -16x * 3x)) = 81 5 + -32x + 48x2 + (-7 + 112x + (3x + -48x2)) = 81 Combine like terms: 112x + 3x = 115x 5 + -32x + 48x2 + (-7 + 115x + -48x2) = 81 Reorder the terms: 5 + -7 + -32x + 115x + 48x2 + -48x2 = 81 Combine like terms: 5 + -7 = -2 -2 + -32x + 115x + 48x2 + -48x2 = 81 Combine like terms: -32x + 115x = 83x -2 + 83x + 48x2 + -48x2 = 81 Combine like terms: 48x2 + -48x2 = 0 -2 + 83x + 0 = 81 -2 + 83x = 81 Solving -2 + 83x = 81 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 83x = 81 + 2 Combine like terms: -2 + 2 = 0 0 + 83x = 81 + 2 83x = 81 + 2 Combine like terms: 81 + 2 = 83 83x = 83 Divide each side by '83'. x = 1 Simplifying x = 1
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