X(3x-6)=(3x+9)(x-6)

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Solution for X(3x-6)=(3x+9)(x-6) equation: 


Simplifying
X(3x + -6) = (3x + 9)(x + -6)

Reorder the terms:
X(-6 + 3x) = (3x + 9)(x + -6)
(-6 * X + 3x * X) = (3x + 9)(x + -6)
(-6X + 3xX) = (3x + 9)(x + -6)

Reorder the terms:
-6X + 3xX = (9 + 3x)(x + -6)

Reorder the terms:
-6X + 3xX = (9 + 3x)(-6 + x)

Multiply (9 + 3x) * (-6 + x)
-6X + 3xX = (9(-6 + x) + 3x * (-6 + x))
-6X + 3xX = ((-6 * 9 + x * 9) + 3x * (-6 + x))
-6X + 3xX = ((-54 + 9x) + 3x * (-6 + x))
-6X + 3xX = (-54 + 9x + (-6 * 3x + x * 3x))
-6X + 3xX = (-54 + 9x + (-18x + 3x2))

Combine like terms: 9x + -18x = -9x
-6X + 3xX = (-54 + -9x + 3x2)

Solving
-6X + 3xX = -54 + -9x + 3x2

Solving for variable 'X'.

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

Reorder the terms:
54 + -6X + 9x + 3xX + -3x2 = -54 + -9x + 3x2 + 54 + 9x + -3x2

Reorder the terms:
54 + -6X + 9x + 3xX + -3x2 = -54 + 54 + -9x + 9x + 3x2 + -3x2

Combine like terms: -54 + 54 = 0
54 + -6X + 9x + 3xX + -3x2 = 0 + -9x + 9x + 3x2 + -3x2
54 + -6X + 9x + 3xX + -3x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
54 + -6X + 9x + 3xX + -3x2 = 0 + 3x2 + -3x2
54 + -6X + 9x + 3xX + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
54 + -6X + 9x + 3xX + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -2X + 3x + xX + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(18 + -2X + 3x + xX + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + -2X + 3x + xX + -1x2 = 0

Solving
18 + -2X + 3x + xX + -1x2 = 0

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

Add '-18' to each side of the equation.
18 + -2X + 3x + xX + -18 + -1x2 = 0 + -18

Reorder the terms:
18 + -18 + -2X + 3x + xX + -1x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -2X + 3x + xX + -1x2 = 0 + -18
-2X + 3x + xX + -1x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-2X + 3x + xX + -1x2 = -18

Add '-3x' to each side of the equation.
-2X + 3x + xX + -3x + -1x2 = -18 + -3x

Reorder the terms:
-2X + 3x + -3x + xX + -1x2 = -18 + -3x

Combine like terms: 3x + -3x = 0
-2X + 0 + xX + -1x2 = -18 + -3x
-2X + xX + -1x2 = -18 + -3x

Add 'x2' to each side of the equation.
-2X + xX + -1x2 + x2 = -18 + -3x + x2

Combine like terms: -1x2 + x2 = 0
-2X + xX + 0 = -18 + -3x + x2
-2X + xX = -18 + -3x + x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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