6x^2=36x-54

Solution for 6x^2=36x-54 equation:

Simplifying
6x2 = 36x + -54

Reorder the terms:
6x2 = -54 + 36x

Solving
6x2 = -54 + 36x

Solving for variable 'x'.

Reorder the terms:
54 + -36x + 6x2 = -54 + 36x + 54 + -36x

Reorder the terms:
54 + -36x + 6x2 = -54 + 54 + 36x + -36x

Combine like terms: -54 + 54 = 0
54 + -36x + 6x2 = 0 + 36x + -36x
54 + -36x + 6x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
54 + -36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + -6x + x2) = 0

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

Ignore the factor 6.
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 '(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
Solution
x = {3, 3}