(x^2-x)(20+x)=100x

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Solution for (x^2-x)(20+x)=100x equation: 


Simplifying
(x2 + -1x)(20 + x) = 100x

Reorder the terms:
(-1x + x2)(20 + x) = 100x

Multiply (-1x + x2) * (20 + x)
(-1x * (20 + x) + x2(20 + x)) = 100x
((20 * -1x + x * -1x) + x2(20 + x)) = 100x
((-20x + -1x2) + x2(20 + x)) = 100x
(-20x + -1x2 + (20 * x2 + x * x2)) = 100x
(-20x + -1x2 + (20x2 + x3)) = 100x

Combine like terms: -1x2 + 20x2 = 19x2
(-20x + 19x2 + x3) = 100x

Solving
-20x + 19x2 + x3 = 100x

Solving for variable 'x'.

Reorder the terms:
-20x + -100x + 19x2 + x3 = 100x + -100x

Combine like terms: -20x + -100x = -120x
-120x + 19x2 + x3 = 100x + -100x

Combine like terms: 100x + -100x = 0
-120x + 19x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-120 + 19x + x2) = 0

Factor a trinomial.
x((-24 + -1x)(5 + -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 '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24

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, -24, 5}

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