(x-2)(x+3)-(x+5)(x-7)=1

Solution for (x-2)(x+3)-(x+5)(x-7)=1 equation:

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