6x^2-61x+1=1

Solution for 6x^2-61x+1=1 equation:

Simplifying
6x2 + -61x + 1 = 1

Reorder the terms:
1 + -61x + 6x2 = 1

Add '-1' to each side of the equation.
1 + -61x + -1 + 6x2 = 1 + -1

Reorder the terms:
1 + -1 + -61x + 6x2 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + -61x + 6x2 = 1 + -1
-61x + 6x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-61x + 6x2 = 0

Solving
-61x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-61 + 6x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-61 + 6x)' equal to zero and attempt to solve:

Simplifying
-61 + 6x = 0

Solving
-61 + 6x = 0

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

Add '61' to each side of the equation.
-61 + 61 + 6x = 0 + 61

Combine like terms: -61 + 61 = 0
0 + 6x = 0 + 61
6x = 0 + 61

Combine like terms: 0 + 61 = 61
6x = 61

Divide each side by '6'.
x = 10.16666667

Simplifying
x = 10.16666667
Solution
x = {0, 10.16666667}