a^2+a=342

Solution for a^2+a=342 equation:

Simplifying
a2 + a = 342

Reorder the terms:
a + a2 = 342

Solving
a + a2 = 342

Solving for variable 'a'.

Reorder the terms:
-342 + a + a2 = 342 + -342

Combine like terms: 342 + -342 = 0
-342 + a + a2 = 0

Factor a trinomial.
(-19 + -1a)(18 + -1a) = 0

Subproblem 1
Set the factor '(-19 + -1a)' equal to zero and attempt to solve:

Simplifying
-19 + -1a = 0

Solving
-19 + -1a = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1a = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1a = 0 + 19
-1a = 0 + 19

Combine like terms: 0 + 19 = 19
-1a = 19

Divide each side by '-1'.
a = -19

Simplifying
a = -19
Subproblem 2
Set the factor '(18 + -1a)' equal to zero and attempt to solve:

Simplifying
18 + -1a = 0

Solving
18 + -1a = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1a = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1a = 0 + -18
-1a = 0 + -18

Combine like terms: 0 + -18 = -18
-1a = -18

Divide each side by '-1'.
a = 18

Simplifying
a = 18
Solution
a = {-19, 18}