x(2x-4)=999(2x+1)(x-2)

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Solution for x(2x-4)=999(2x+1)(x-2) equation: 


Simplifying
x(2x + -4) = 999(2x + 1)(x + -2)

Reorder the terms:
x(-4 + 2x) = 999(2x + 1)(x + -2)
(-4 * x + 2x * x) = 999(2x + 1)(x + -2)
(-4x + 2x2) = 999(2x + 1)(x + -2)

Reorder the terms:
-4x + 2x2 = 999(1 + 2x)(x + -2)

Reorder the terms:
-4x + 2x2 = 999(1 + 2x)(-2 + x)

Multiply (1 + 2x) * (-2 + x)
-4x + 2x2 = 999(1(-2 + x) + 2x * (-2 + x))
-4x + 2x2 = 999((-2 * 1 + x * 1) + 2x * (-2 + x))
-4x + 2x2 = 999((-2 + 1x) + 2x * (-2 + x))
-4x + 2x2 = 999(-2 + 1x + (-2 * 2x + x * 2x))
-4x + 2x2 = 999(-2 + 1x + (-4x + 2x2))

Combine like terms: 1x + -4x = -3x
-4x + 2x2 = 999(-2 + -3x + 2x2)
-4x + 2x2 = (-2 * 999 + -3x * 999 + 2x2 * 999)
-4x + 2x2 = (-1998 + -2997x + 1998x2)

Solving
-4x + 2x2 = -1998 + -2997x + 1998x2

Solving for variable 'x'.

Reorder the terms:
1998 + -4x + 2997x + 2x2 + -1998x2 = -1998 + -2997x + 1998x2 + 1998 + 2997x + -1998x2

Combine like terms: -4x + 2997x = 2993x
1998 + 2993x + 2x2 + -1998x2 = -1998 + -2997x + 1998x2 + 1998 + 2997x + -1998x2

Combine like terms: 2x2 + -1998x2 = -1996x2
1998 + 2993x + -1996x2 = -1998 + -2997x + 1998x2 + 1998 + 2997x + -1998x2

Reorder the terms:
1998 + 2993x + -1996x2 = -1998 + 1998 + -2997x + 2997x + 1998x2 + -1998x2

Combine like terms: -1998 + 1998 = 0
1998 + 2993x + -1996x2 = 0 + -2997x + 2997x + 1998x2 + -1998x2
1998 + 2993x + -1996x2 = -2997x + 2997x + 1998x2 + -1998x2

Combine like terms: -2997x + 2997x = 0
1998 + 2993x + -1996x2 = 0 + 1998x2 + -1998x2
1998 + 2993x + -1996x2 = 1998x2 + -1998x2

Combine like terms: 1998x2 + -1998x2 = 0
1998 + 2993x + -1996x2 = 0

Factor a trinomial.
(2 + -1x)(999 + 1996x) = 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 '(999 + 1996x)' equal to zero and attempt to solve:

Simplifying
999 + 1996x = 0

Solving
999 + 1996x = 0

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

Add '-999' to each side of the equation.
999 + -999 + 1996x = 0 + -999

Combine like terms: 999 + -999 = 0
0 + 1996x = 0 + -999
1996x = 0 + -999

Combine like terms: 0 + -999 = -999
1996x = -999

Divide each side by '1996'.
x = -0.500501002

Simplifying
x = -0.500501002
Solution
x = {2, -0.500501002}

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