x^3-24*x^2+144*x=x^3-20*x^2+100*x

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Solution for x^3-24*x^2+144*x=x^3-20*x^2+100*x equation: 


Simplifying
x3 + -24x2 + 144x = x3 + -20x2 + 100x

Reorder the terms:
144x + -24x2 + x3 = x3 + -20x2 + 100x

Reorder the terms:
144x + -24x2 + x3 = 100x + -20x2 + x3

Add '-1x3' to each side of the equation.
144x + -24x2 + x3 + -1x3 = 100x + -20x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
144x + -24x2 + 0 = 100x + -20x2 + x3 + -1x3
144x + -24x2 = 100x + -20x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
144x + -24x2 = 100x + -20x2 + 0
144x + -24x2 = 100x + -20x2

Solving
144x + -24x2 = 100x + -20x2

Solving for variable 'x'.

Reorder the terms:
144x + -100x + -24x2 + 20x2 = 100x + -20x2 + -100x + 20x2

Combine like terms: 144x + -100x = 44x
44x + -24x2 + 20x2 = 100x + -20x2 + -100x + 20x2

Combine like terms: -24x2 + 20x2 = -4x2
44x + -4x2 = 100x + -20x2 + -100x + 20x2

Reorder the terms:
44x + -4x2 = 100x + -100x + -20x2 + 20x2

Combine like terms: 100x + -100x = 0
44x + -4x2 = 0 + -20x2 + 20x2
44x + -4x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
44x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {0, 11}

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