3x^2-18x=165

Solution for 3x^2-18x=165 equation:

Simplifying
3x2 + -18x = 165

Reorder the terms:
-18x + 3x2 = 165

Solving
-18x + 3x2 = 165

Solving for variable 'x'.

Reorder the terms:
-165 + -18x + 3x2 = 165 + -165

Combine like terms: 165 + -165 = 0
-165 + -18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-55 + -6x + x2) = 0

Factor a trinomial.
3((-5 + -1x)(11 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-5, 11}