(x-1)[x-2(x-3)]=x(1-x)

Solution for (x-1)[x-2(x-3)]=x(1-x) equation:

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

Reorder the terms:
(-1 + x)[x + -2(x + -3)] = x(1 + -1x)

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

Reorder the terms:
(-1 + x)[6 + x + -2x] = x(1 + -1x)

Combine like terms: x + -2x = -1x
(-1 + x)[6 + -1x] = x(1 + -1x)

Multiply (-1 + x) * [6 + -1x]
(-1[6 + -1x] + x[6 + -1x]) = x(1 + -1x)
([6 * -1 + -1x * -1] + x[6 + -1x]) = x(1 + -1x)
([-6 + 1x] + x[6 + -1x]) = x(1 + -1x)
(-6 + 1x + [6 * x + -1x * x]) = x(1 + -1x)
(-6 + 1x + [6x + -1x2]) = x(1 + -1x)

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

Add 'x2' to each side of the equation.
-6 + 7x + -1x2 + x2 = 1x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-6 + 7x + 0 = 1x + -1x2 + x2
-6 + 7x = 1x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-6 + 7x = 1x + 0
-6 + 7x = 1x

Solving
-6 + 7x = 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
-6 + 7x + -1x = 1x + -1x

Combine like terms: 7x + -1x = 6x
-6 + 6x = 1x + -1x

Combine like terms: 1x + -1x = 0
-6 + 6x = 0

Add '6' to each side of the equation.
-6 + 6 + 6x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 6x = 0 + 6
6x = 0 + 6

Combine like terms: 0 + 6 = 6
6x = 6

Divide each side by '6'.
x = 1

Simplifying
x = 1