r^2+42r=0

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

Simplifying
r2 + 42r = 0

Reorder the terms:
42r + r2 = 0

Solving
42r + r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(42 + r) = 0

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(42 + r)' equal to zero and attempt to solve:

Simplifying
42 + r = 0

Solving
42 + r = 0

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

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

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

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

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