(x-7)(x-6)=(x+1)(x-9)+1

Solution for (x-7)(x-6)=(x+1)(x-9)+1 equation:

Simplifying
(x + -7)(x + -6) = (x + 1)(x + -9) + 1

Reorder the terms:
(-7 + x)(x + -6) = (x + 1)(x + -9) + 1

Reorder the terms:
(-7 + x)(-6 + x) = (x + 1)(x + -9) + 1

Multiply (-7 + x) * (-6 + x)
(-7(-6 + x) + x(-6 + x)) = (x + 1)(x + -9) + 1
((-6 * -7 + x * -7) + x(-6 + x)) = (x + 1)(x + -9) + 1
((42 + -7x) + x(-6 + x)) = (x + 1)(x + -9) + 1
(42 + -7x + (-6 * x + x * x)) = (x + 1)(x + -9) + 1
(42 + -7x + (-6x + x2)) = (x + 1)(x + -9) + 1

Combine like terms: -7x + -6x = -13x
(42 + -13x + x2) = (x + 1)(x + -9) + 1

Reorder the terms:
42 + -13x + x2 = (1 + x)(x + -9) + 1

Reorder the terms:
42 + -13x + x2 = (1 + x)(-9 + x) + 1

Multiply (1 + x) * (-9 + x)
42 + -13x + x2 = (1(-9 + x) + x(-9 + x)) + 1
42 + -13x + x2 = ((-9 * 1 + x * 1) + x(-9 + x)) + 1
42 + -13x + x2 = ((-9 + 1x) + x(-9 + x)) + 1
42 + -13x + x2 = (-9 + 1x + (-9 * x + x * x)) + 1
42 + -13x + x2 = (-9 + 1x + (-9x + x2)) + 1

Combine like terms: 1x + -9x = -8x
42 + -13x + x2 = (-9 + -8x + x2) + 1

Reorder the terms:
42 + -13x + x2 = -9 + 1 + -8x + x2

Combine like terms: -9 + 1 = -8
42 + -13x + x2 = -8 + -8x + x2

Add '-1x2' to each side of the equation.
42 + -13x + x2 + -1x2 = -8 + -8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + -13x + 0 = -8 + -8x + x2 + -1x2
42 + -13x = -8 + -8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + -13x = -8 + -8x + 0
42 + -13x = -8 + -8x

Solving
42 + -13x = -8 + -8x

Solving for variable 'x'.

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

Add '8x' to each side of the equation.
42 + -13x + 8x = -8 + -8x + 8x

Combine like terms: -13x + 8x = -5x
42 + -5x = -8 + -8x + 8x

Combine like terms: -8x + 8x = 0
42 + -5x = -8 + 0
42 + -5x = -8

Add '-42' to each side of the equation.
42 + -42 + -5x = -8 + -42

Combine like terms: 42 + -42 = 0
0 + -5x = -8 + -42
-5x = -8 + -42

Combine like terms: -8 + -42 = -50
-5x = -50

Divide each side by '-5'.
x = 10

Simplifying
x = 10