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

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


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

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

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

Multiply (-4 + x) * (-2 + x)
(-4(-2 + x) + x(-2 + x)) = 3
((-2 * -4 + x * -4) + x(-2 + x)) = 3
((8 + -4x) + x(-2 + x)) = 3
(8 + -4x + (-2 * x + x * x)) = 3
(8 + -4x + (-2x + x2)) = 3

Combine like terms: -4x + -2x = -6x
(8 + -6x + x2) = 3

Solving
8 + -6x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
8 + -3 + -6x + x2 = 3 + -3

Combine like terms: 8 + -3 = 5
5 + -6x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
5 + -6x + x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}

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