200x^4=-800x^3+9000x^2

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Solution for 200x^4=-800x^3+9000x^2 equation: 


Simplifying
200x4 = -800x3 + 9000x2

Reorder the terms:
200x4 = 9000x2 + -800x3

Solving
200x4 = 9000x2 + -800x3

Solving for variable 'x'.

Reorder the terms:
-9000x2 + 800x3 + 200x4 = 9000x2 + -800x3 + -9000x2 + 800x3

Reorder the terms:
-9000x2 + 800x3 + 200x4 = 9000x2 + -9000x2 + -800x3 + 800x3

Combine like terms: 9000x2 + -9000x2 = 0
-9000x2 + 800x3 + 200x4 = 0 + -800x3 + 800x3
-9000x2 + 800x3 + 200x4 = -800x3 + 800x3

Combine like terms: -800x3 + 800x3 = 0
-9000x2 + 800x3 + 200x4 = 0

Factor out the Greatest Common Factor (GCF), '200x2'.
200x2(-45 + 4x + x2) = 0

Factor a trinomial.
200x2((-9 + -1x)(5 + -1x)) = 0

Ignore the factor 200.

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 '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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, -9, 5}

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