0=x^4-x^3-20x^2

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Solution for 0=x^4-x^3-20x^2 equation: 


Simplifying
0 = x4 + -1x3 + -20x2

Reorder the terms:
0 = -20x2 + -1x3 + x4

Solving
0 = -20x2 + -1x3 + x4

Solving for variable 'x'.
Remove the zero:
20x2 + x3 + -1x4 = -20x2 + -1x3 + x4 + 20x2 + x3 + -1x4

Reorder the terms:
20x2 + x3 + -1x4 = -20x2 + 20x2 + -1x3 + x3 + x4 + -1x4

Combine like terms: -20x2 + 20x2 = 0
20x2 + x3 + -1x4 = 0 + -1x3 + x3 + x4 + -1x4
20x2 + x3 + -1x4 = -1x3 + x3 + x4 + -1x4

Combine like terms: -1x3 + x3 = 0
20x2 + x3 + -1x4 = 0 + x4 + -1x4
20x2 + x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
20x2 + x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(20 + x + -1x2) = 0

Factor a trinomial.
x2((5 + -1x)(4 + x)) = 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, 5, -4}

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