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

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


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

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

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

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

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

Solving
8 + -6x + x2 = 3x

Solving for variable 'x'.

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

Combine like terms: -6x + -3x = -9x
8 + -9x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
8 + -9x + x2 = 0

Factor a trinomial.
(1 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {1, 8}

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