(5-x)(5x^2-x^3)=

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Solution for (5-x)(5x^2-x^3)= equation: 


Simplifying
(5 + -1x)(5x2 + -1x3) = 0

Multiply (5 + -1x) * (5x2 + -1x3)
(5(5x2 + -1x3) + -1x * (5x2 + -1x3)) = 0
((5x2 * 5 + -1x3 * 5) + -1x * (5x2 + -1x3)) = 0
((25x2 + -5x3) + -1x * (5x2 + -1x3)) = 0
(25x2 + -5x3 + (5x2 * -1x + -1x3 * -1x)) = 0
(25x2 + -5x3 + (-5x3 + 1x4)) = 0

Combine like terms: -5x3 + -5x3 = -10x3
(25x2 + -10x3 + 1x4) = 0

Solving
25x2 + -10x3 + 1x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(25 + -10x + x2) = 0

Factor a trinomial.
x2((5 + -1x)(5 + -1x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 5, 5}

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