3x^2=18x-27

Solution for 3x^2=18x-27 equation:

Simplifying
3x2 = 18x + -27

Reorder the terms:
3x2 = -27 + 18x

Solving
3x2 = -27 + 18x

Solving for variable 'x'.

Reorder the terms:
27 + -18x + 3x2 = -27 + 18x + 27 + -18x

Reorder the terms:
27 + -18x + 3x2 = -27 + 27 + 18x + -18x

Combine like terms: -27 + 27 = 0
27 + -18x + 3x2 = 0 + 18x + -18x
27 + -18x + 3x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
27 + -18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -6x + x2) = 0

Factor a trinomial.
3((3 + -1x)(3 + -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 '(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}