2x(x-1)=6x(x-9)

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Solution for 2x(x-1)=6x(x-9) equation: 


Simplifying
2x(x + -1) = 6x(x + -9)

Reorder the terms:
2x(-1 + x) = 6x(x + -9)
(-1 * 2x + x * 2x) = 6x(x + -9)
(-2x + 2x2) = 6x(x + -9)

Reorder the terms:
-2x + 2x2 = 6x(-9 + x)
-2x + 2x2 = (-9 * 6x + x * 6x)
-2x + 2x2 = (-54x + 6x2)

Solving
-2x + 2x2 = -54x + 6x2

Solving for variable 'x'.

Reorder the terms:
-2x + 54x + 2x2 + -6x2 = -54x + 6x2 + 54x + -6x2

Combine like terms: -2x + 54x = 52x
52x + 2x2 + -6x2 = -54x + 6x2 + 54x + -6x2

Combine like terms: 2x2 + -6x2 = -4x2
52x + -4x2 = -54x + 6x2 + 54x + -6x2

Reorder the terms:
52x + -4x2 = -54x + 54x + 6x2 + -6x2

Combine like terms: -54x + 54x = 0
52x + -4x2 = 0 + 6x2 + -6x2
52x + -4x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
52x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(13 + -1x) = 0

Ignore the factor 4.

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 '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {0, 13}

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