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Simplifying (3x + -2)(x + -5) = 4 + (3x + -6)(x + 7) Reorder the terms: (-2 + 3x)(x + -5) = 4 + (3x + -6)(x + 7) Reorder the terms: (-2 + 3x)(-5 + x) = 4 + (3x + -6)(x + 7) Multiply (-2 + 3x) * (-5 + x) (-2(-5 + x) + 3x * (-5 + x)) = 4 + (3x + -6)(x + 7) ((-5 * -2 + x * -2) + 3x * (-5 + x)) = 4 + (3x + -6)(x + 7) ((10 + -2x) + 3x * (-5 + x)) = 4 + (3x + -6)(x + 7) (10 + -2x + (-5 * 3x + x * 3x)) = 4 + (3x + -6)(x + 7) (10 + -2x + (-15x + 3x2)) = 4 + (3x + -6)(x + 7) Combine like terms: -2x + -15x = -17x (10 + -17x + 3x2) = 4 + (3x + -6)(x + 7) Reorder the terms: 10 + -17x + 3x2 = 4 + (-6 + 3x)(x + 7) Reorder the terms: 10 + -17x + 3x2 = 4 + (-6 + 3x)(7 + x) Multiply (-6 + 3x) * (7 + x) 10 + -17x + 3x2 = 4 + (-6(7 + x) + 3x * (7 + x)) 10 + -17x + 3x2 = 4 + ((7 * -6 + x * -6) + 3x * (7 + x)) 10 + -17x + 3x2 = 4 + ((-42 + -6x) + 3x * (7 + x)) 10 + -17x + 3x2 = 4 + (-42 + -6x + (7 * 3x + x * 3x)) 10 + -17x + 3x2 = 4 + (-42 + -6x + (21x + 3x2)) Combine like terms: -6x + 21x = 15x 10 + -17x + 3x2 = 4 + (-42 + 15x + 3x2) Combine like terms: 4 + -42 = -38 10 + -17x + 3x2 = -38 + 15x + 3x2 Add '-3x2' to each side of the equation. 10 + -17x + 3x2 + -3x2 = -38 + 15x + 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 10 + -17x + 0 = -38 + 15x + 3x2 + -3x2 10 + -17x = -38 + 15x + 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 10 + -17x = -38 + 15x + 0 10 + -17x = -38 + 15x Solving 10 + -17x = -38 + 15x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15x' to each side of the equation. 10 + -17x + -15x = -38 + 15x + -15x Combine like terms: -17x + -15x = -32x 10 + -32x = -38 + 15x + -15x Combine like terms: 15x + -15x = 0 10 + -32x = -38 + 0 10 + -32x = -38 Add '-10' to each side of the equation. 10 + -10 + -32x = -38 + -10 Combine like terms: 10 + -10 = 0 0 + -32x = -38 + -10 -32x = -38 + -10 Combine like terms: -38 + -10 = -48 -32x = -48 Divide each side by '-32'. x = 1.5 Simplifying x = 1.5
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