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Simplifying (x + 3)(x + -2) + -1(x + -3)(x + 2) + -5 = 6x + -7 Reorder the terms: (3 + x)(x + -2) + -1(x + -3)(x + 2) + -5 = 6x + -7 Reorder the terms: (3 + x)(-2 + x) + -1(x + -3)(x + 2) + -5 = 6x + -7 Multiply (3 + x) * (-2 + x) (3(-2 + x) + x(-2 + x)) + -1(x + -3)(x + 2) + -5 = 6x + -7 ((-2 * 3 + x * 3) + x(-2 + x)) + -1(x + -3)(x + 2) + -5 = 6x + -7 ((-6 + 3x) + x(-2 + x)) + -1(x + -3)(x + 2) + -5 = 6x + -7 (-6 + 3x + (-2 * x + x * x)) + -1(x + -3)(x + 2) + -5 = 6x + -7 (-6 + 3x + (-2x + x2)) + -1(x + -3)(x + 2) + -5 = 6x + -7 Combine like terms: 3x + -2x = 1x (-6 + 1x + x2) + -1(x + -3)(x + 2) + -5 = 6x + -7 Reorder the terms: -6 + 1x + x2 + -1(-3 + x)(x + 2) + -5 = 6x + -7 Reorder the terms: -6 + 1x + x2 + -1(-3 + x)(2 + x) + -5 = 6x + -7 Multiply (-3 + x) * (2 + x) -6 + 1x + x2 + -1(-3(2 + x) + x(2 + x)) + -5 = 6x + -7 -6 + 1x + x2 + -1((2 * -3 + x * -3) + x(2 + x)) + -5 = 6x + -7 -6 + 1x + x2 + -1((-6 + -3x) + x(2 + x)) + -5 = 6x + -7 -6 + 1x + x2 + -1(-6 + -3x + (2 * x + x * x)) + -5 = 6x + -7 -6 + 1x + x2 + -1(-6 + -3x + (2x + x2)) + -5 = 6x + -7 Combine like terms: -3x + 2x = -1x -6 + 1x + x2 + -1(-6 + -1x + x2) + -5 = 6x + -7 -6 + 1x + x2 + (-6 * -1 + -1x * -1 + x2 * -1) + -5 = 6x + -7 -6 + 1x + x2 + (6 + 1x + -1x2) + -5 = 6x + -7 Reorder the terms: -6 + 6 + -5 + 1x + 1x + x2 + -1x2 = 6x + -7 Combine like terms: -6 + 6 = 0 0 + -5 + 1x + 1x + x2 + -1x2 = 6x + -7 -5 + 1x + 1x + x2 + -1x2 = 6x + -7 Combine like terms: 1x + 1x = 2x -5 + 2x + x2 + -1x2 = 6x + -7 Combine like terms: x2 + -1x2 = 0 -5 + 2x + 0 = 6x + -7 -5 + 2x = 6x + -7 Reorder the terms: -5 + 2x = -7 + 6x Solving -5 + 2x = -7 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. -5 + 2x + -6x = -7 + 6x + -6x Combine like terms: 2x + -6x = -4x -5 + -4x = -7 + 6x + -6x Combine like terms: 6x + -6x = 0 -5 + -4x = -7 + 0 -5 + -4x = -7 Add '5' to each side of the equation. -5 + 5 + -4x = -7 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = -7 + 5 -4x = -7 + 5 Combine like terms: -7 + 5 = -2 -4x = -2 Divide each side by '-4'. x = 0.5 Simplifying x = 0.5
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