x(x+2)=x(x+6)(x+4)

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Solution for x(x+2)=x(x+6)(x+4) equation: 


Simplifying
x(x + 2) = x(x + 6)(x + 4)

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

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

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

Multiply (6 + x) * (4 + x)
2x + x2 = x(6(4 + x) + x(4 + x))
2x + x2 = x((4 * 6 + x * 6) + x(4 + x))
2x + x2 = x((24 + 6x) + x(4 + x))
2x + x2 = x(24 + 6x + (4 * x + x * x))
2x + x2 = x(24 + 6x + (4x + x2))

Combine like terms: 6x + 4x = 10x
2x + x2 = x(24 + 10x + x2)
2x + x2 = (24 * x + 10x * x + x2 * x)
2x + x2 = (24x + 10x2 + x3)

Solving
2x + x2 = 24x + 10x2 + x3

Solving for variable 'x'.

Reorder the terms:
2x + -24x + x2 + -10x2 + -1x3 = 24x + 10x2 + x3 + -24x + -10x2 + -1x3

Combine like terms: 2x + -24x = -22x
-22x + x2 + -10x2 + -1x3 = 24x + 10x2 + x3 + -24x + -10x2 + -1x3

Combine like terms: x2 + -10x2 = -9x2
-22x + -9x2 + -1x3 = 24x + 10x2 + x3 + -24x + -10x2 + -1x3

Reorder the terms:
-22x + -9x2 + -1x3 = 24x + -24x + 10x2 + -10x2 + x3 + -1x3

Combine like terms: 24x + -24x = 0
-22x + -9x2 + -1x3 = 0 + 10x2 + -10x2 + x3 + -1x3
-22x + -9x2 + -1x3 = 10x2 + -10x2 + x3 + -1x3

Combine like terms: 10x2 + -10x2 = 0
-22x + -9x2 + -1x3 = 0 + x3 + -1x3
-22x + -9x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-22x + -9x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(22 + 9x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(22 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
22 + 9x + x2 = 0

Solving
22 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 9x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + 9x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 9x + x2 = 0 + -22
9x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
9x + x2 = -22

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -22 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -22 + 20.25

Combine like terms: -22 + 20.25 = -1.75
20.25 + 9x + x2 = -1.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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