2X+(X-2)(X-4)=X+2

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Solution for 2X+(X-2)(X-4)=X+2 equation: 


Simplifying
2X + (X + -2)(X + -4) = X + 2

Reorder the terms:
2X + (-2 + X)(X + -4) = X + 2

Reorder the terms:
2X + (-2 + X)(-4 + X) = X + 2

Multiply (-2 + X) * (-4 + X)
2X + (-2(-4 + X) + X(-4 + X)) = X + 2
2X + ((-4 * -2 + X * -2) + X(-4 + X)) = X + 2
2X + ((8 + -2X) + X(-4 + X)) = X + 2
2X + (8 + -2X + (-4 * X + X * X)) = X + 2
2X + (8 + -2X + (-4X + X2)) = X + 2

Combine like terms: -2X + -4X = -6X
2X + (8 + -6X + X2) = X + 2

Reorder the terms:
8 + 2X + -6X + X2 = X + 2

Combine like terms: 2X + -6X = -4X
8 + -4X + X2 = X + 2

Reorder the terms:
8 + -4X + X2 = 2 + X

Solving
8 + -4X + X2 = 2 + X

Solving for variable 'X'.

Reorder the terms:
8 + -2 + -4X + -1X + X2 = 2 + X + -2 + -1X

Combine like terms: 8 + -2 = 6
6 + -4X + -1X + X2 = 2 + X + -2 + -1X

Combine like terms: -4X + -1X = -5X
6 + -5X + X2 = 2 + X + -2 + -1X

Reorder the terms:
6 + -5X + X2 = 2 + -2 + X + -1X

Combine like terms: 2 + -2 = 0
6 + -5X + X2 = 0 + X + -1X
6 + -5X + X2 = X + -1X

Combine like terms: X + -1X = 0
6 + -5X + X2 = 0

Factor a trinomial.
(2 + -1X)(3 + -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 '(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 = {2, 3}

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