x^3+49x^2=0

Solution for x^3+49x^2=0 equation:

Simplifying
x3 + 49x2 = 0

Reorder the terms:
49x2 + x3 = 0

Solving
49x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(49 + x) = 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 '(49 + x)' equal to zero and attempt to solve:

Simplifying
49 + x = 0

Solving
49 + x = 0

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

Add '-49' to each side of the equation.
49 + -49 + x = 0 + -49

Combine like terms: 49 + -49 = 0
0 + x = 0 + -49
x = 0 + -49

Combine like terms: 0 + -49 = -49
x = -49

Simplifying
x = -49
Solution
x = {0, -49}