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

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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 = -5x
(6 + -5x + x2) + -1(x + 5)(x + -7) = 1

Reorder the terms:
6 + -5x + x2 + -1(5 + x)(x + -7) = 1

Reorder the terms:
6 + -5x + x2 + -1(5 + x)(-7 + x) = 1

Multiply (5 + x) * (-7 + x)
6 + -5x + x2 + -1(5(-7 + x) + x(-7 + x)) = 1
6 + -5x + x2 + -1((-7 * 5 + x * 5) + x(-7 + x)) = 1
6 + -5x + x2 + -1((-35 + 5x) + x(-7 + x)) = 1
6 + -5x + x2 + -1(-35 + 5x + (-7 * x + x * x)) = 1
6 + -5x + x2 + -1(-35 + 5x + (-7x + x2)) = 1

Combine like terms: 5x + -7x = -2x
6 + -5x + x2 + -1(-35 + -2x + x2) = 1
6 + -5x + x2 + (-35 * -1 + -2x * -1 + x2 * -1) = 1
6 + -5x + x2 + (35 + 2x + -1x2) = 1

Reorder the terms:
6 + 35 + -5x + 2x + x2 + -1x2 = 1

Combine like terms: 6 + 35 = 41
41 + -5x + 2x + x2 + -1x2 = 1

Combine like terms: -5x + 2x = -3x
41 + -3x + x2 + -1x2 = 1

Combine like terms: x2 + -1x2 = 0
41 + -3x + 0 = 1
41 + -3x = 1

Solving
41 + -3x = 1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-41' to each side of the equation.
41 + -41 + -3x = 1 + -41

Combine like terms: 41 + -41 = 0
0 + -3x = 1 + -41
-3x = 1 + -41

Combine like terms: 1 + -41 = -40
-3x = -40

Divide each side by '-3'.
x = 13.33333333

Simplifying
x = 13.33333333

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