0=x^4+10x^3+24x^2

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Solution for 0=x^4+10x^3+24x^2 equation: 


Simplifying
0 = x4 + 10x3 + 24x2

Reorder the terms:
0 = 24x2 + 10x3 + x4

Solving
0 = 24x2 + 10x3 + x4

Solving for variable 'x'.
Remove the zero:
-24x2 + -10x3 + -1x4 = 24x2 + 10x3 + x4 + -24x2 + -10x3 + -1x4

Reorder the terms:
-24x2 + -10x3 + -1x4 = 24x2 + -24x2 + 10x3 + -10x3 + x4 + -1x4

Combine like terms: 24x2 + -24x2 = 0
-24x2 + -10x3 + -1x4 = 0 + 10x3 + -10x3 + x4 + -1x4
-24x2 + -10x3 + -1x4 = 10x3 + -10x3 + x4 + -1x4

Combine like terms: 10x3 + -10x3 = 0
-24x2 + -10x3 + -1x4 = 0 + x4 + -1x4
-24x2 + -10x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-24x2 + -10x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1x2'.
-1x2(24 + 10x + x2) = 0

Factor a trinomial.
-1x2((6 + x)(4 + x)) = 0

Ignore the factor -1.

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 '(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, -6, -4}

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