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Simplifying (x + -1)(x + 5) + -1(x + 2)(x + -3) = 3(1 + 5x) Reorder the terms: (-1 + x)(x + 5) + -1(x + 2)(x + -3) = 3(1 + 5x) Reorder the terms: (-1 + x)(5 + x) + -1(x + 2)(x + -3) = 3(1 + 5x) Multiply (-1 + x) * (5 + x) (-1(5 + x) + x(5 + x)) + -1(x + 2)(x + -3) = 3(1 + 5x) ((5 * -1 + x * -1) + x(5 + x)) + -1(x + 2)(x + -3) = 3(1 + 5x) ((-5 + -1x) + x(5 + x)) + -1(x + 2)(x + -3) = 3(1 + 5x) (-5 + -1x + (5 * x + x * x)) + -1(x + 2)(x + -3) = 3(1 + 5x) (-5 + -1x + (5x + x2)) + -1(x + 2)(x + -3) = 3(1 + 5x) Combine like terms: -1x + 5x = 4x (-5 + 4x + x2) + -1(x + 2)(x + -3) = 3(1 + 5x) Reorder the terms: -5 + 4x + x2 + -1(2 + x)(x + -3) = 3(1 + 5x) Reorder the terms: -5 + 4x + x2 + -1(2 + x)(-3 + x) = 3(1 + 5x) Multiply (2 + x) * (-3 + x) -5 + 4x + x2 + -1(2(-3 + x) + x(-3 + x)) = 3(1 + 5x) -5 + 4x + x2 + -1((-3 * 2 + x * 2) + x(-3 + x)) = 3(1 + 5x) -5 + 4x + x2 + -1((-6 + 2x) + x(-3 + x)) = 3(1 + 5x) -5 + 4x + x2 + -1(-6 + 2x + (-3 * x + x * x)) = 3(1 + 5x) -5 + 4x + x2 + -1(-6 + 2x + (-3x + x2)) = 3(1 + 5x) Combine like terms: 2x + -3x = -1x -5 + 4x + x2 + -1(-6 + -1x + x2) = 3(1 + 5x) -5 + 4x + x2 + (-6 * -1 + -1x * -1 + x2 * -1) = 3(1 + 5x) -5 + 4x + x2 + (6 + 1x + -1x2) = 3(1 + 5x) Reorder the terms: -5 + 6 + 4x + 1x + x2 + -1x2 = 3(1 + 5x) Combine like terms: -5 + 6 = 1 1 + 4x + 1x + x2 + -1x2 = 3(1 + 5x) Combine like terms: 4x + 1x = 5x 1 + 5x + x2 + -1x2 = 3(1 + 5x) Combine like terms: x2 + -1x2 = 0 1 + 5x + 0 = 3(1 + 5x) 1 + 5x = 3(1 + 5x) 1 + 5x = (1 * 3 + 5x * 3) 1 + 5x = (3 + 15x) Solving 1 + 5x = 3 + 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. 1 + 5x + -15x = 3 + 15x + -15x Combine like terms: 5x + -15x = -10x 1 + -10x = 3 + 15x + -15x Combine like terms: 15x + -15x = 0 1 + -10x = 3 + 0 1 + -10x = 3 Add '-1' to each side of the equation. 1 + -1 + -10x = 3 + -1 Combine like terms: 1 + -1 = 0 0 + -10x = 3 + -1 -10x = 3 + -1 Combine like terms: 3 + -1 = 2 -10x = 2 Divide each side by '-10'. x = -0.2 Simplifying x = -0.2
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