3x^2-36x+121=13

Solution for 3x^2-36x+121=13 equation:

Simplifying
3x2 + -36x + 121 = 13

Reorder the terms:
121 + -36x + 3x2 = 13

Solving
121 + -36x + 3x2 = 13

Solving for variable 'x'.

Reorder the terms:
121 + -13 + -36x + 3x2 = 13 + -13

Combine like terms: 121 + -13 = 108
108 + -36x + 3x2 = 13 + -13

Combine like terms: 13 + -13 = 0
108 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(36 + -12x + x2) = 0

Factor a trinomial.
3((6 + -1x)(6 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
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 = {6, 6}