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Simplifying (x + -2)(x + 3) + -1(x + 5)(x + -7) = 1 Reorder the terms: (-2 + x)(x + 3) + -1(x + 5)(x + -7) = 1 Reorder the terms: (-2 + x)(3 + x) + -1(x + 5)(x + -7) = 1 Multiply (-2 + x) * (3 + x) (-2(3 + x) + x(3 + x)) + -1(x + 5)(x + -7) = 1 ((3 * -2 + x * -2) + x(3 + x)) + -1(x + 5)(x + -7) = 1 ((-6 + -2x) + x(3 + x)) + -1(x + 5)(x + -7) = 1 (-6 + -2x + (3 * x + x * x)) + -1(x + 5)(x + -7) = 1 (-6 + -2x + (3x + x2)) + -1(x + 5)(x + -7) = 1 Combine like terms: -2x + 3x = 1x (-6 + 1x + x2) + -1(x + 5)(x + -7) = 1 Reorder the terms: -6 + 1x + x2 + -1(5 + x)(x + -7) = 1 Reorder the terms: -6 + 1x + x2 + -1(5 + x)(-7 + x) = 1 Multiply (5 + x) * (-7 + x) -6 + 1x + x2 + -1(5(-7 + x) + x(-7 + x)) = 1 -6 + 1x + x2 + -1((-7 * 5 + x * 5) + x(-7 + x)) = 1 -6 + 1x + x2 + -1((-35 + 5x) + x(-7 + x)) = 1 -6 + 1x + x2 + -1(-35 + 5x + (-7 * x + x * x)) = 1 -6 + 1x + x2 + -1(-35 + 5x + (-7x + x2)) = 1 Combine like terms: 5x + -7x = -2x -6 + 1x + x2 + -1(-35 + -2x + x2) = 1 -6 + 1x + x2 + (-35 * -1 + -2x * -1 + x2 * -1) = 1 -6 + 1x + x2 + (35 + 2x + -1x2) = 1 Reorder the terms: -6 + 35 + 1x + 2x + x2 + -1x2 = 1 Combine like terms: -6 + 35 = 29 29 + 1x + 2x + x2 + -1x2 = 1 Combine like terms: 1x + 2x = 3x 29 + 3x + x2 + -1x2 = 1 Combine like terms: x2 + -1x2 = 0 29 + 3x + 0 = 1 29 + 3x = 1 Solving 29 + 3x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 3x = 1 + -29 Combine like terms: 29 + -29 = 0 0 + 3x = 1 + -29 3x = 1 + -29 Combine like terms: 1 + -29 = -28 3x = -28 Divide each side by '3'. x = -9.333333333 Simplifying x = -9.333333333
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