4a^2-4a-41=-6

Solution for 4a^2-4a-41=-6 equation:

Simplifying
4a2 + -4a + -41 = -6

Reorder the terms:
-41 + -4a + 4a2 = -6

Solving
-41 + -4a + 4a2 = -6

Solving for variable 'a'.

Reorder the terms:
-41 + 6 + -4a + 4a2 = -6 + 6

Combine like terms: -41 + 6 = -35
-35 + -4a + 4a2 = -6 + 6

Combine like terms: -6 + 6 = 0
-35 + -4a + 4a2 = 0

Factor a trinomial.
(-5 + -2a)(7 + -2a) = 0

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

Simplifying
-5 + -2a = 0

Solving
-5 + -2a = 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 + -2a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2a = 0 + 5
-2a = 0 + 5

Combine like terms: 0 + 5 = 5
-2a = 5

Divide each side by '-2'.
a = -2.5

Simplifying
a = -2.5
Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve:

Simplifying
7 + -2a = 0

Solving
7 + -2a = 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 + -2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2a = 0 + -7
-2a = 0 + -7

Combine like terms: 0 + -7 = -7
-2a = -7

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {-2.5, 3.5}