3x^2-27x+61=1

Solution for 3x^2-27x+61=1 equation:

Simplifying
3x2 + -27x + 61 = 1

Reorder the terms:
61 + -27x + 3x2 = 1

Solving
61 + -27x + 3x2 = 1

Solving for variable 'x'.

Reorder the terms:
61 + -1 + -27x + 3x2 = 1 + -1

Combine like terms: 61 + -1 = 60
60 + -27x + 3x2 = 1 + -1

Combine like terms: 1 + -1 = 0
60 + -27x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -9x + x2) = 0

Factor a trinomial.
3((4 + -1x)(5 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

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

Simplifying
x = 5
Solution
x = {4, 5}