(24x+60)(x^4+10x^3+25x^2)=0

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Solution for (24x+60)(x^4+10x^3+25x^2)=0 equation: 


Simplifying
(24x + 60)(x4 + 10x3 + 25x2) = 0

Reorder the terms:
(60 + 24x)(x4 + 10x3 + 25x2) = 0

Reorder the terms:
(60 + 24x)(25x2 + 10x3 + x4) = 0

Multiply (60 + 24x) * (25x2 + 10x3 + x4)
(60(25x2 + 10x3 + x4) + 24x * (25x2 + 10x3 + x4)) = 0
((25x2 * 60 + 10x3 * 60 + x4 * 60) + 24x * (25x2 + 10x3 + x4)) = 0
((1500x2 + 600x3 + 60x4) + 24x * (25x2 + 10x3 + x4)) = 0
(1500x2 + 600x3 + 60x4 + (25x2 * 24x + 10x3 * 24x + x4 * 24x)) = 0
(1500x2 + 600x3 + 60x4 + (600x3 + 240x4 + 24x5)) = 0

Reorder the terms:
(1500x2 + 600x3 + 600x3 + 60x4 + 240x4 + 24x5) = 0

Combine like terms: 600x3 + 600x3 = 1200x3
(1500x2 + 1200x3 + 60x4 + 240x4 + 24x5) = 0

Combine like terms: 60x4 + 240x4 = 300x4
(1500x2 + 1200x3 + 300x4 + 24x5) = 0

Solving
1500x2 + 1200x3 + 300x4 + 24x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x2'.
12x2(125 + 100x + 25x2 + 2x3) = 0

Ignore the factor 12.

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 '(125 + 100x + 25x2 + 2x3)' equal to zero and attempt to solve:

Simplifying
125 + 100x + 25x2 + 2x3 = 0

Solving
125 + 100x + 25x2 + 2x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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