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Simplifying (5x + -3)(2x + -3) + -2(4x + -1)(x + -3) = (2x + -3)(x + 5) Reorder the terms: (-3 + 5x)(2x + -3) + -2(4x + -1)(x + -3) = (2x + -3)(x + 5) Reorder the terms: (-3 + 5x)(-3 + 2x) + -2(4x + -1)(x + -3) = (2x + -3)(x + 5) Multiply (-3 + 5x) * (-3 + 2x) (-3(-3 + 2x) + 5x * (-3 + 2x)) + -2(4x + -1)(x + -3) = (2x + -3)(x + 5) ((-3 * -3 + 2x * -3) + 5x * (-3 + 2x)) + -2(4x + -1)(x + -3) = (2x + -3)(x + 5) ((9 + -6x) + 5x * (-3 + 2x)) + -2(4x + -1)(x + -3) = (2x + -3)(x + 5) (9 + -6x + (-3 * 5x + 2x * 5x)) + -2(4x + -1)(x + -3) = (2x + -3)(x + 5) (9 + -6x + (-15x + 10x2)) + -2(4x + -1)(x + -3) = (2x + -3)(x + 5) Combine like terms: -6x + -15x = -21x (9 + -21x + 10x2) + -2(4x + -1)(x + -3) = (2x + -3)(x + 5) Reorder the terms: 9 + -21x + 10x2 + -2(-1 + 4x)(x + -3) = (2x + -3)(x + 5) Reorder the terms: 9 + -21x + 10x2 + -2(-1 + 4x)(-3 + x) = (2x + -3)(x + 5) Multiply (-1 + 4x) * (-3 + x) 9 + -21x + 10x2 + -2(-1(-3 + x) + 4x * (-3 + x)) = (2x + -3)(x + 5) 9 + -21x + 10x2 + -2((-3 * -1 + x * -1) + 4x * (-3 + x)) = (2x + -3)(x + 5) 9 + -21x + 10x2 + -2((3 + -1x) + 4x * (-3 + x)) = (2x + -3)(x + 5) 9 + -21x + 10x2 + -2(3 + -1x + (-3 * 4x + x * 4x)) = (2x + -3)(x + 5) 9 + -21x + 10x2 + -2(3 + -1x + (-12x + 4x2)) = (2x + -3)(x + 5) Combine like terms: -1x + -12x = -13x 9 + -21x + 10x2 + -2(3 + -13x + 4x2) = (2x + -3)(x + 5) 9 + -21x + 10x2 + (3 * -2 + -13x * -2 + 4x2 * -2) = (2x + -3)(x + 5) 9 + -21x + 10x2 + (-6 + 26x + -8x2) = (2x + -3)(x + 5) Reorder the terms: 9 + -6 + -21x + 26x + 10x2 + -8x2 = (2x + -3)(x + 5) Combine like terms: 9 + -6 = 3 3 + -21x + 26x + 10x2 + -8x2 = (2x + -3)(x + 5) Combine like terms: -21x + 26x = 5x 3 + 5x + 10x2 + -8x2 = (2x + -3)(x + 5) Combine like terms: 10x2 + -8x2 = 2x2 3 + 5x + 2x2 = (2x + -3)(x + 5) Reorder the terms: 3 + 5x + 2x2 = (-3 + 2x)(x + 5) Reorder the terms: 3 + 5x + 2x2 = (-3 + 2x)(5 + x) Multiply (-3 + 2x) * (5 + x) 3 + 5x + 2x2 = (-3(5 + x) + 2x * (5 + x)) 3 + 5x + 2x2 = ((5 * -3 + x * -3) + 2x * (5 + x)) 3 + 5x + 2x2 = ((-15 + -3x) + 2x * (5 + x)) 3 + 5x + 2x2 = (-15 + -3x + (5 * 2x + x * 2x)) 3 + 5x + 2x2 = (-15 + -3x + (10x + 2x2)) Combine like terms: -3x + 10x = 7x 3 + 5x + 2x2 = (-15 + 7x + 2x2) Add '-2x2' to each side of the equation. 3 + 5x + 2x2 + -2x2 = -15 + 7x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 3 + 5x + 0 = -15 + 7x + 2x2 + -2x2 3 + 5x = -15 + 7x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 3 + 5x = -15 + 7x + 0 3 + 5x = -15 + 7x Solving 3 + 5x = -15 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. 3 + 5x + -7x = -15 + 7x + -7x Combine like terms: 5x + -7x = -2x 3 + -2x = -15 + 7x + -7x Combine like terms: 7x + -7x = 0 3 + -2x = -15 + 0 3 + -2x = -15 Add '-3' to each side of the equation. 3 + -3 + -2x = -15 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = -15 + -3 -2x = -15 + -3 Combine like terms: -15 + -3 = -18 -2x = -18 Divide each side by '-2'. x = 9 Simplifying x = 9
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