3x^2=36x-81

Solution for 3x^2=36x-81 equation:

Simplifying
3x2 = 36x + -81

Reorder the terms:
3x2 = -81 + 36x

Solving
3x2 = -81 + 36x

Solving for variable 'x'.

Reorder the terms:
81 + -36x + 3x2 = -81 + 36x + 81 + -36x

Reorder the terms:
81 + -36x + 3x2 = -81 + 81 + 36x + -36x

Combine like terms: -81 + 81 = 0
81 + -36x + 3x2 = 0 + 36x + -36x
81 + -36x + 3x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
81 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + -12x + x2) = 0

Factor a trinomial.
3((3 + -1x)(9 + -1x)) = 0

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {3, 9}