7x^2=41x+6

Solution for 7x^2=41x+6 equation:

Simplifying
7x2 = 41x + 6

Reorder the terms:
7x2 = 6 + 41x

Solving
7x2 = 6 + 41x

Solving for variable 'x'.

Reorder the terms:
-6 + -41x + 7x2 = 6 + 41x + -6 + -41x

Reorder the terms:
-6 + -41x + 7x2 = 6 + -6 + 41x + -41x

Combine like terms: 6 + -6 = 0
-6 + -41x + 7x2 = 0 + 41x + -41x
-6 + -41x + 7x2 = 41x + -41x

Combine like terms: 41x + -41x = 0
-6 + -41x + 7x2 = 0

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

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

Simplifying
-1 + -7x = 0

Solving
-1 + -7x = 0

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

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

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

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

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

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

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

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

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

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

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