42x+x^2=0

Solution for 42x+x^2=0 equation:

Simplifying
42x + x2 = 0

Solving
42x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(42 + 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 '(42 + x)' equal to zero and attempt to solve:

Simplifying
42 + x = 0

Solving
42 + x = 0

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

Add '-42' to each side of the equation.
42 + -42 + x = 0 + -42

Combine like terms: 42 + -42 = 0
0 + x = 0 + -42
x = 0 + -42

Combine like terms: 0 + -42 = -42
x = -42

Simplifying
x = -42
Solution
x = {0, -42}