x(x-2)=x(x+4)12

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Solution for x(x-2)=x(x+4)12 equation: 


Simplifying
x(x + -2) = x(x + 4) * 12

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

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

Reorder the terms for easier multiplication:
-2x + x2 = 12x(4 + x)
-2x + x2 = (4 * 12x + x * 12x)
-2x + x2 = (48x + 12x2)

Solving
-2x + x2 = 48x + 12x2

Solving for variable 'x'.

Reorder the terms:
-2x + -48x + x2 + -12x2 = 48x + 12x2 + -48x + -12x2

Combine like terms: -2x + -48x = -50x
-50x + x2 + -12x2 = 48x + 12x2 + -48x + -12x2

Combine like terms: x2 + -12x2 = -11x2
-50x + -11x2 = 48x + 12x2 + -48x + -12x2

Reorder the terms:
-50x + -11x2 = 48x + -48x + 12x2 + -12x2

Combine like terms: 48x + -48x = 0
-50x + -11x2 = 0 + 12x2 + -12x2
-50x + -11x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-50x + -11x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(50 + 11x) = 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 '(50 + 11x)' equal to zero and attempt to solve:

Simplifying
50 + 11x = 0

Solving
50 + 11x = 0

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

Add '-50' to each side of the equation.
50 + -50 + 11x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + 11x = 0 + -50
11x = 0 + -50

Combine like terms: 0 + -50 = -50
11x = -50

Divide each side by '11'.
x = -4.545454545

Simplifying
x = -4.545454545
Solution
x = {0, -4.545454545}

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