x^2+61x=0

Solution for x^2+61x=0 equation:

Simplifying
x2 + 61x = 0

Reorder the terms:
61x + x2 = 0

Solving
61x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(61 + 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 '(61 + x)' equal to zero and attempt to solve:

Simplifying
61 + x = 0

Solving
61 + x = 0

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

Add '-61' to each side of the equation.
61 + -61 + x = 0 + -61

Combine like terms: 61 + -61 = 0
0 + x = 0 + -61
x = 0 + -61

Combine like terms: 0 + -61 = -61
x = -61

Simplifying
x = -61
Solution
x = {0, -61}