(x-4)(x-3)=x

Solution for (x-4)(x-3)=x equation:

Simplifying
(x + -4)(x + -3) = x

Reorder the terms:
(-4 + x)(x + -3) = x

Reorder the terms:
(-4 + x)(-3 + x) = x

Multiply (-4 + x) * (-3 + x)
(-4(-3 + x) + x(-3 + x)) = x
((-3 * -4 + x * -4) + x(-3 + x)) = x
((12 + -4x) + x(-3 + x)) = x
(12 + -4x + (-3 * x + x * x)) = x
(12 + -4x + (-3x + x2)) = x

Combine like terms: -4x + -3x = -7x
(12 + -7x + x2) = x

Solving
12 + -7x + x2 = x

Solving for variable 'x'.

Reorder the terms:
12 + -7x + -1x + x2 = x + -1x

Combine like terms: -7x + -1x = -8x
12 + -8x + x2 = x + -1x

Combine like terms: x + -1x = 0
12 + -8x + x2 = 0

Factor a trinomial.
(2 + -1x)(6 + -1x) = 0

Subproblem 1
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
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 = {2, 6}