x^2+24x+x=0

Solution for x^2+24x+x=0 equation:

Simplifying
x2 + 24x + x = 0

Reorder the terms:
24x + x + x2 = 0

Combine like terms: 24x + x = 25x
25x + x2 = 0

Solving
25x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(25 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(25 + x)' equal to zero and attempt to solve:

Simplifying
25 + x = 0

Solving
25 + x = 0

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

Add '-25' to each side of the equation.
25 + -25 + x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + x = 0 + -25
x = 0 + -25

Combine like terms: 0 + -25 = -25
x = -25

Simplifying
x = -25
Solution
x = {0, -25}