(X-3)4-(X-7)6=1

Solution for (X-3)4-(X-7)6=1 equation:

Simplifying
(X + -3) * 4 + -1(X + -7) * 6 = 1

Reorder the terms:
(-3 + X) * 4 + -1(X + -7) * 6 = 1

Reorder the terms for easier multiplication:
4(-3 + X) + -1(X + -7) * 6 = 1
(-3 * 4 + X * 4) + -1(X + -7) * 6 = 1
(-12 + 4X) + -1(X + -7) * 6 = 1

Reorder the terms:
-12 + 4X + -1(-7 + X) * 6 = 1

Reorder the terms for easier multiplication:
-12 + 4X + -1 * 6(-7 + X) = 1

Multiply -1 * 6
-12 + 4X + -6(-7 + X) = 1
-12 + 4X + (-7 * -6 + X * -6) = 1
-12 + 4X + (42 + -6X) = 1

Reorder the terms:
-12 + 42 + 4X + -6X = 1

Combine like terms: -12 + 42 = 30
30 + 4X + -6X = 1

Combine like terms: 4X + -6X = -2X
30 + -2X = 1

Solving
30 + -2X = 1

Solving for variable 'X'.

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

Add '-30' to each side of the equation.
30 + -30 + -2X = 1 + -30

Combine like terms: 30 + -30 = 0
0 + -2X = 1 + -30
-2X = 1 + -30

Combine like terms: 1 + -30 = -29
-2X = -29

Divide each side by '-2'.
X = 14.5

Simplifying
X = 14.5