9x^2-9x=54

Solution for 9x^2-9x=54 equation:

Simplifying
9x2 + -9x = 54

Reorder the terms:
-9x + 9x2 = 54

Solving
-9x + 9x2 = 54

Solving for variable 'x'.

Reorder the terms:
-54 + -9x + 9x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + -9x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-6 + -1x + x2) = 0

Factor a trinomial.
9((-2 + -1x)(3 + -1x)) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
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 = {-2, 3}