2x(x-6)=x(x-4)

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


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

Reorder the terms:
2x(-6 + x) = x(x + -4)
(-6 * 2x + x * 2x) = x(x + -4)
(-12x + 2x2) = x(x + -4)

Reorder the terms:
-12x + 2x2 = x(-4 + x)
-12x + 2x2 = (-4 * x + x * x)
-12x + 2x2 = (-4x + x2)

Solving
-12x + 2x2 = -4x + x2

Solving for variable 'x'.

Reorder the terms:
-12x + 4x + 2x2 + -1x2 = -4x + x2 + 4x + -1x2

Combine like terms: -12x + 4x = -8x
-8x + 2x2 + -1x2 = -4x + x2 + 4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-8x + 1x2 = -4x + x2 + 4x + -1x2

Reorder the terms:
-8x + 1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
-8x + 1x2 = 0 + x2 + -1x2
-8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + x) = 0


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 '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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