-400x^3+2100x^2=100x^4

Solution for -400x^3+2100x^2=100x^4 equation:

Simplifying
-400x3 + 2100x2 = 100x4

Reorder the terms:
2100x2 + -400x3 = 100x4

Solving
2100x2 + -400x3 = 100x4

Solving for variable 'x'.

Combine like terms: 100x4 + -100x4 = 0
2100x2 + -400x3 + -100x4 = 0

Factor out the Greatest Common Factor (GCF), '100x2'.
100x2(21 + -4x + -1x2) = 0

Factor a trinomial.
100x2((3 + -1x)(7 + x)) = 0

Ignore the factor 100.
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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 3
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {0, 3, -7}