5x^4+30x^3+10x^2=4x^2-x^3

Solution for 5x^4+30x^3+10x^2=4x^2-x^3 equation:

Simplifying
5x4 + 30x3 + 10x2 = 4x2 + -1x3

Reorder the terms:
10x2 + 30x3 + 5x4 = 4x2 + -1x3

Solving
10x2 + 30x3 + 5x4 = 4x2 + -1x3

Solving for variable 'x'.

Reorder the terms:
10x2 + -4x2 + 30x3 + x3 + 5x4 = 4x2 + -1x3 + -4x2 + x3

Combine like terms: 10x2 + -4x2 = 6x2
6x2 + 30x3 + x3 + 5x4 = 4x2 + -1x3 + -4x2 + x3

Combine like terms: 30x3 + x3 = 31x3
6x2 + 31x3 + 5x4 = 4x2 + -1x3 + -4x2 + x3

Reorder the terms:
6x2 + 31x3 + 5x4 = 4x2 + -4x2 + -1x3 + x3

Combine like terms: 4x2 + -4x2 = 0
6x2 + 31x3 + 5x4 = 0 + -1x3 + x3
6x2 + 31x3 + 5x4 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
6x2 + 31x3 + 5x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(6 + 31x + 5x2) = 0

Factor a trinomial.
x2((6 + x)(1 + 5x)) = 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 3
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 0

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

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

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

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

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {0, -6, -0.2}