3(x-4)-x(x-4)=0

Solution for 3(x-4)-x(x-4)=0 equation:

Simplifying
3(x + -4) + -1x(x + -4) = 0

Reorder the terms:
3(-4 + x) + -1x(x + -4) = 0
(-4 * 3 + x * 3) + -1x(x + -4) = 0
(-12 + 3x) + -1x(x + -4) = 0

Reorder the terms:
-12 + 3x + -1x(-4 + x) = 0
-12 + 3x + (-4 * -1x + x * -1x) = 0
-12 + 3x + (4x + -1x2) = 0

Combine like terms: 3x + 4x = 7x
-12 + 7x + -1x2 = 0

Solving
-12 + 7x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {4, 3}