3x^2-54=-9x

Solution for 3x^2-54=-9x equation:

Simplifying
3x2 + -54 = -9x

Reorder the terms:
-54 + 3x2 = -9x

Solving
-54 + 3x2 = -9x

Solving for variable 'x'.

Reorder the terms:
-54 + 9x + 3x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-54 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + 3x + x2) = 0

Factor a trinomial.
3((-6 + -1x)(3 + -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 '(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 = {-6, 3}