6-[3-2(x+5)]=5-2[3-(6+x)]

Solution for 6-[3-2(x+5)]=5-2[3-(6+x)] equation:

Simplifying
6 + -1[3 + -2(x + 5)] = 5 + -2[3 + -1(6 + x)]

Reorder the terms:
6 + -1[3 + -2(5 + x)] = 5 + -2[3 + -1(6 + x)]
6 + -1[3 + (5 * -2 + x * -2)] = 5 + -2[3 + -1(6 + x)]
6 + -1[3 + (-10 + -2x)] = 5 + -2[3 + -1(6 + x)]

Combine like terms: 3 + -10 = -7
6 + -1[-7 + -2x] = 5 + -2[3 + -1(6 + x)]
6 + [-7 * -1 + -2x * -1] = 5 + -2[3 + -1(6 + x)]
6 + [7 + 2x] = 5 + -2[3 + -1(6 + x)]

Combine like terms: 6 + 7 = 13
13 + 2x = 5 + -2[3 + -1(6 + x)]
13 + 2x = 5 + -2[3 + (6 * -1 + x * -1)]
13 + 2x = 5 + -2[3 + (-6 + -1x)]

Combine like terms: 3 + -6 = -3
13 + 2x = 5 + -2[-3 + -1x]
13 + 2x = 5 + [-3 * -2 + -1x * -2]
13 + 2x = 5 + [6 + 2x]

Combine like terms: 5 + 6 = 11
13 + 2x = 11 + 2x

Add '-2x' to each side of the equation.
13 + 2x + -2x = 11 + 2x + -2x

Combine like terms: 2x + -2x = 0
13 + 0 = 11 + 2x + -2x
13 = 11 + 2x + -2x

Combine like terms: 2x + -2x = 0
13 = 11 + 0
13 = 11

Solving
13 = 11

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.