42a^2+a=0

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

Simplifying
42a2 + a = 0

Reorder the terms:
a + 42a2 = 0

Solving
a + 42a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(1 + 42a) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(1 + 42a)' equal to zero and attempt to solve:

Simplifying
1 + 42a = 0

Solving
1 + 42a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 42a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 42a = 0 + -1
42a = 0 + -1

Combine like terms: 0 + -1 = -1
42a = -1

Divide each side by '42'.
a = -0.02380952381

Simplifying
a = -0.02380952381
Solution
a = {0, -0.02380952381}