(x-4)2-(6-x)2=1

Solution for (x-4)2-(6-x)2=1 equation:

Simplifying
(x + -4) * 2 + -1(6 + -1x) * 2 = 1

Reorder the terms:
(-4 + x) * 2 + -1(6 + -1x) * 2 = 1

Reorder the terms for easier multiplication:
2(-4 + x) + -1(6 + -1x) * 2 = 1
(-4 * 2 + x * 2) + -1(6 + -1x) * 2 = 1
(-8 + 2x) + -1(6 + -1x) * 2 = 1

Reorder the terms for easier multiplication:
-8 + 2x + -1 * 2(6 + -1x) = 1

Multiply -1 * 2
-8 + 2x + -2(6 + -1x) = 1
-8 + 2x + (6 * -2 + -1x * -2) = 1
-8 + 2x + (-12 + 2x) = 1

Reorder the terms:
-8 + -12 + 2x + 2x = 1

Combine like terms: -8 + -12 = -20
-20 + 2x + 2x = 1

Combine like terms: 2x + 2x = 4x
-20 + 4x = 1

Solving
-20 + 4x = 1

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + 4x = 1 + 20

Combine like terms: -20 + 20 = 0
0 + 4x = 1 + 20
4x = 1 + 20

Combine like terms: 1 + 20 = 21
4x = 21

Divide each side by '4'.
x = 5.25

Simplifying
x = 5.25