x(x-4)=3(x-2)

Solution for x(x-4)=3(x-2) equation:

Simplifying
x(x + -4) = 3(x + -2)

Reorder the terms:
x(-4 + x) = 3(x + -2)
(-4 * x + x * x) = 3(x + -2)
(-4x + x2) = 3(x + -2)

Reorder the terms:
-4x + x2 = 3(-2 + x)
-4x + x2 = (-2 * 3 + x * 3)
-4x + x2 = (-6 + 3x)

Solving
-4x + x2 = -6 + 3x

Solving for variable 'x'.

Reorder the terms:
6 + -4x + -3x + x2 = -6 + 3x + 6 + -3x

Combine like terms: -4x + -3x = -7x
6 + -7x + x2 = -6 + 3x + 6 + -3x

Reorder the terms:
6 + -7x + x2 = -6 + 6 + 3x + -3x

Combine like terms: -6 + 6 = 0
6 + -7x + x2 = 0 + 3x + -3x
6 + -7x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 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}