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Simplifying (3x + -1)(3x + -1) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) Reorder the terms: (-1 + 3x)(3x + -1) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) Reorder the terms: (-1 + 3x)(-1 + 3x) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) Multiply (-1 + 3x) * (-1 + 3x) (-1(-1 + 3x) + 3x * (-1 + 3x)) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) ((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) ((1 + -3x) + 3x * (-1 + 3x)) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) (1 + -3x + (-1 * 3x + 3x * 3x)) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) (1 + -3x + (-3x + 9x2)) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) Combine like terms: -3x + -3x = -6x (1 + -6x + 9x2) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) Reorder the terms: 1 + -6x + 9x2 + -3(3 + 2x)(2x + 3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) Reorder the terms: 1 + -6x + 9x2 + -3(3 + 2x)(3 + 2x) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) Multiply (3 + 2x) * (3 + 2x) 1 + -6x + 9x2 + -3(3(3 + 2x) + 2x * (3 + 2x)) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) 1 + -6x + 9x2 + -3((3 * 3 + 2x * 3) + 2x * (3 + 2x)) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) 1 + -6x + 9x2 + -3((9 + 6x) + 2x * (3 + 2x)) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) 1 + -6x + 9x2 + -3(9 + 6x + (3 * 2x + 2x * 2x)) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) 1 + -6x + 9x2 + -3(9 + 6x + (6x + 4x2)) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) Combine like terms: 6x + 6x = 12x 1 + -6x + 9x2 + -3(9 + 12x + 4x2) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) 1 + -6x + 9x2 + (9 * -3 + 12x * -3 + 4x2 * -3) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) 1 + -6x + 9x2 + (-27 + -36x + -12x2) + 42 = 2x(-1x + -5) + -1(x + -1)(x + -1) Reorder the terms: 1 + -27 + 42 + -6x + -36x + 9x2 + -12x2 = 2x(-1x + -5) + -1(x + -1)(x + -1) Combine like terms: 1 + -27 = -26 -26 + 42 + -6x + -36x + 9x2 + -12x2 = 2x(-1x + -5) + -1(x + -1)(x + -1) Combine like terms: -26 + 42 = 16 16 + -6x + -36x + 9x2 + -12x2 = 2x(-1x + -5) + -1(x + -1)(x + -1) Combine like terms: -6x + -36x = -42x 16 + -42x + 9x2 + -12x2 = 2x(-1x + -5) + -1(x + -1)(x + -1) Combine like terms: 9x2 + -12x2 = -3x2 16 + -42x + -3x2 = 2x(-1x + -5) + -1(x + -1)(x + -1) Reorder the terms: 16 + -42x + -3x2 = 2x(-5 + -1x) + -1(x + -1)(x + -1) 16 + -42x + -3x2 = (-5 * 2x + -1x * 2x) + -1(x + -1)(x + -1) 16 + -42x + -3x2 = (-10x + -2x2) + -1(x + -1)(x + -1) Reorder the terms: 16 + -42x + -3x2 = -10x + -2x2 + -1(-1 + x)(x + -1) Reorder the terms: 16 + -42x + -3x2 = -10x + -2x2 + -1(-1 + x)(-1 + x) Multiply (-1 + x) * (-1 + x) 16 + -42x + -3x2 = -10x + -2x2 + -1(-1(-1 + x) + x(-1 + x)) 16 + -42x + -3x2 = -10x + -2x2 + -1((-1 * -1 + x * -1) + x(-1 + x)) 16 + -42x + -3x2 = -10x + -2x2 + -1((1 + -1x) + x(-1 + x)) 16 + -42x + -3x2 = -10x + -2x2 + -1(1 + -1x + (-1 * x + x * x)) 16 + -42x + -3x2 = -10x + -2x2 + -1(1 + -1x + (-1x + x2)) Combine like terms: -1x + -1x = -2x 16 + -42x + -3x2 = -10x + -2x2 + -1(1 + -2x + x2) 16 + -42x + -3x2 = -10x + -2x2 + (1 * -1 + -2x * -1 + x2 * -1) 16 + -42x + -3x2 = -10x + -2x2 + (-1 + 2x + -1x2) Reorder the terms: 16 + -42x + -3x2 = -1 + -10x + 2x + -2x2 + -1x2 Combine like terms: -10x + 2x = -8x 16 + -42x + -3x2 = -1 + -8x + -2x2 + -1x2 Combine like terms: -2x2 + -1x2 = -3x2 16 + -42x + -3x2 = -1 + -8x + -3x2 Add '3x2' to each side of the equation. 16 + -42x + -3x2 + 3x2 = -1 + -8x + -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 16 + -42x + 0 = -1 + -8x + -3x2 + 3x2 16 + -42x = -1 + -8x + -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 16 + -42x = -1 + -8x + 0 16 + -42x = -1 + -8x Solving 16 + -42x = -1 + -8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8x' to each side of the equation. 16 + -42x + 8x = -1 + -8x + 8x Combine like terms: -42x + 8x = -34x 16 + -34x = -1 + -8x + 8x Combine like terms: -8x + 8x = 0 16 + -34x = -1 + 0 16 + -34x = -1 Add '-16' to each side of the equation. 16 + -16 + -34x = -1 + -16 Combine like terms: 16 + -16 = 0 0 + -34x = -1 + -16 -34x = -1 + -16 Combine like terms: -1 + -16 = -17 -34x = -17 Divide each side by '-34'. x = 0.5 Simplifying x = 0.5
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