0-4x=x^2(x-4)

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Solution for 0-4x=x^2(x-4) equation: 


Simplifying
0 + -4x = x2(x + -4)
Remove the zero:
-4x = x2(x + -4)

Reorder the terms:
-4x = x2(-4 + x)
-4x = (-4 * x2 + x * x2)
-4x = (-4x2 + x3)

Solving
-4x = -4x2 + x3

Solving for variable 'x'.

Reorder the terms:
-4x + 4x2 + -1x3 = -4x2 + 4x2 + x3 + -1x3

Combine like terms: -4x2 + 4x2 = 0
-4x + 4x2 + -1x3 = 0 + x3 + -1x3
-4x + 4x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-4x + 4x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 4x + -1x2) = 0

Factor a trinomial.
x((-2 + x)(2 + -1x)) = 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 2, 2}

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