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Simplifying (3x + 4)(2x + -5) + -122 = (6x + -1)(x + 10) Reorder the terms: (4 + 3x)(2x + -5) + -122 = (6x + -1)(x + 10) Reorder the terms: (4 + 3x)(-5 + 2x) + -122 = (6x + -1)(x + 10) Multiply (4 + 3x) * (-5 + 2x) (4(-5 + 2x) + 3x * (-5 + 2x)) + -122 = (6x + -1)(x + 10) ((-5 * 4 + 2x * 4) + 3x * (-5 + 2x)) + -122 = (6x + -1)(x + 10) ((-20 + 8x) + 3x * (-5 + 2x)) + -122 = (6x + -1)(x + 10) (-20 + 8x + (-5 * 3x + 2x * 3x)) + -122 = (6x + -1)(x + 10) (-20 + 8x + (-15x + 6x2)) + -122 = (6x + -1)(x + 10) Combine like terms: 8x + -15x = -7x (-20 + -7x + 6x2) + -122 = (6x + -1)(x + 10) Reorder the terms: -20 + -122 + -7x + 6x2 = (6x + -1)(x + 10) Combine like terms: -20 + -122 = -142 -142 + -7x + 6x2 = (6x + -1)(x + 10) Reorder the terms: -142 + -7x + 6x2 = (-1 + 6x)(x + 10) Reorder the terms: -142 + -7x + 6x2 = (-1 + 6x)(10 + x) Multiply (-1 + 6x) * (10 + x) -142 + -7x + 6x2 = (-1(10 + x) + 6x * (10 + x)) -142 + -7x + 6x2 = ((10 * -1 + x * -1) + 6x * (10 + x)) -142 + -7x + 6x2 = ((-10 + -1x) + 6x * (10 + x)) -142 + -7x + 6x2 = (-10 + -1x + (10 * 6x + x * 6x)) -142 + -7x + 6x2 = (-10 + -1x + (60x + 6x2)) Combine like terms: -1x + 60x = 59x -142 + -7x + 6x2 = (-10 + 59x + 6x2) Add '-6x2' to each side of the equation. -142 + -7x + 6x2 + -6x2 = -10 + 59x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -142 + -7x + 0 = -10 + 59x + 6x2 + -6x2 -142 + -7x = -10 + 59x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -142 + -7x = -10 + 59x + 0 -142 + -7x = -10 + 59x Solving -142 + -7x = -10 + 59x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-59x' to each side of the equation. -142 + -7x + -59x = -10 + 59x + -59x Combine like terms: -7x + -59x = -66x -142 + -66x = -10 + 59x + -59x Combine like terms: 59x + -59x = 0 -142 + -66x = -10 + 0 -142 + -66x = -10 Add '142' to each side of the equation. -142 + 142 + -66x = -10 + 142 Combine like terms: -142 + 142 = 0 0 + -66x = -10 + 142 -66x = -10 + 142 Combine like terms: -10 + 142 = 132 -66x = 132 Divide each side by '-66'. x = -2 Simplifying x = -2
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