a^2+2a-41=-6

Solution for a^2+2a-41=-6 equation:

Simplifying
a2 + 2a + -41 = -6

Reorder the terms:
-41 + 2a + a2 = -6

Solving
-41 + 2a + a2 = -6

Solving for variable 'a'.

Reorder the terms:
-41 + 6 + 2a + a2 = -6 + 6

Combine like terms: -41 + 6 = -35
-35 + 2a + a2 = -6 + 6

Combine like terms: -6 + 6 = 0
-35 + 2a + a2 = 0

Factor a trinomial.
(-7 + -1a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve:

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-7, 5}