x^2=-64x

Solution for x^2=-64x equation:

Simplifying
x2 = -64x

Solving
x2 = -64x

Solving for variable 'x'.

Reorder the terms:
64x + x2 = -64x + 64x

Combine like terms: -64x + 64x = 0
64x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(64 + 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 '(64 + x)' equal to zero and attempt to solve:

Simplifying
64 + x = 0

Solving
64 + x = 0

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

Add '-64' to each side of the equation.
64 + -64 + x = 0 + -64

Combine like terms: 64 + -64 = 0
0 + x = 0 + -64
x = 0 + -64

Combine like terms: 0 + -64 = -64
x = -64

Simplifying
x = -64
Solution
x = {0, -64}