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

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

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

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

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

Multiply (-1 + x) * (-6 + x)
(-1(-6 + x) + x(-6 + x)) = -2x(x + -1)
((-6 * -1 + x * -1) + x(-6 + x)) = -2x(x + -1)
((6 + -1x) + x(-6 + x)) = -2x(x + -1)
(6 + -1x + (-6 * x + x * x)) = -2x(x + -1)
(6 + -1x + (-6x + x2)) = -2x(x + -1)

Combine like terms: -1x + -6x = -7x
(6 + -7x + x2) = -2x(x + -1)

Reorder the terms:
6 + -7x + x2 = -2x(-1 + x)
6 + -7x + x2 = (-1 * -2x + x * -2x)
6 + -7x + x2 = (2x + -2x2)

Solving
6 + -7x + x2 = 2x + -2x2

Solving for variable 'x'.

Reorder the terms:
6 + -7x + -2x + x2 + 2x2 = 2x + -2x2 + -2x + 2x2

Combine like terms: -7x + -2x = -9x
6 + -9x + x2 + 2x2 = 2x + -2x2 + -2x + 2x2

Combine like terms: x2 + 2x2 = 3x2
6 + -9x + 3x2 = 2x + -2x2 + -2x + 2x2

Reorder the terms:
6 + -9x + 3x2 = 2x + -2x + -2x2 + 2x2

Combine like terms: 2x + -2x = 0
6 + -9x + 3x2 = 0 + -2x2 + 2x2
6 + -9x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
6 + -9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -3x + x2) = 0

Factor a trinomial.
3((1 + -1x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}