(x-2)(x-3)=2x

Solution for (x-2)(x-3)=2x equation:

Simplifying
(x + -2)(x + -3) = 2x

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

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

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) = 2x
((-3 * -2 + x * -2) + x(-3 + x)) = 2x
((6 + -2x) + x(-3 + x)) = 2x
(6 + -2x + (-3 * x + x * x)) = 2x
(6 + -2x + (-3x + x2)) = 2x

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) = 2x

Solving
6 + -5x + x2 = 2x

Solving for variable 'x'.

Reorder the terms:
6 + -5x + -2x + x2 = 2x + -2x

Combine like terms: -5x + -2x = -7x
6 + -7x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + -7x + x2 = 0

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

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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1, 6}