7a^2-6=41a

Solution for 7a^2-6=41a equation:

Simplifying
7a2 + -6 = 41a

Reorder the terms:
-6 + 7a2 = 41a

Solving
-6 + 7a2 = 41a

Solving for variable 'a'.

Reorder the terms:
-6 + -41a + 7a2 = 41a + -41a

Combine like terms: 41a + -41a = 0
-6 + -41a + 7a2 = 0

Factor a trinomial.
(-1 + -7a)(6 + -1a) = 0

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

Simplifying
-1 + -7a = 0

Solving
-1 + -7a = 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 + -7a = 0 + 1

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

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

Divide each side by '-7'.
a = -0.1428571429

Simplifying
a = -0.1428571429
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-0.1428571429, 6}