6x(x-1)=1-x

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

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

Reorder the terms:
6x(-1 + x) = 1 + -1x
(-1 * 6x + x * 6x) = 1 + -1x
(-6x + 6x2) = 1 + -1x

Solving
-6x + 6x2 = 1 + -1x

Solving for variable 'x'.

Reorder the terms:
-1 + -6x + x + 6x2 = 1 + -1x + -1 + x

Combine like terms: -6x + x = -5x
-1 + -5x + 6x2 = 1 + -1x + -1 + x

Reorder the terms:
-1 + -5x + 6x2 = 1 + -1 + -1x + x

Combine like terms: 1 + -1 = 0
-1 + -5x + 6x2 = 0 + -1x + x
-1 + -5x + 6x2 = -1x + x

Combine like terms: -1x + x = 0
-1 + -5x + 6x2 = 0

Factor a trinomial.
(-1 + -6x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -6x = 0 + 1

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

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

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-0.1666666667, 1}