4.6x=-x^2

Solution for 4.6x=-x^2 equation:

Simplifying
4.6x = -1x2

Solving
4.6x = -1x2

Solving for variable 'x'.

Combine like terms: -1x2 + x2 = 0
4.6x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(4.6 + 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 '(4.6 + x)' equal to zero and attempt to solve:

Simplifying
4.6 + x = 0

Solving
4.6 + x = 0

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

Add '-4.6' to each side of the equation.
4.6 + -4.6 + x = 0 + -4.6

Combine like terms: 4.6 + -4.6 = 0.0
0.0 + x = 0 + -4.6
x = 0 + -4.6

Combine like terms: 0 + -4.6 = -4.6
x = -4.6

Simplifying
x = -4.6
Solution
x = {0, -4.6}