6x^2=51x+165

Solution for 6x^2=51x+165 equation:

Simplifying
6x2 = 51x + 165

Reorder the terms:
6x2 = 165 + 51x

Solving
6x2 = 165 + 51x

Solving for variable 'x'.

Reorder the terms:
-165 + -51x + 6x2 = 165 + 51x + -165 + -51x

Reorder the terms:
-165 + -51x + 6x2 = 165 + -165 + 51x + -51x

Combine like terms: 165 + -165 = 0
-165 + -51x + 6x2 = 0 + 51x + -51x
-165 + -51x + 6x2 = 51x + -51x

Combine like terms: 51x + -51x = 0
-165 + -51x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-55 + -17x + 2x2) = 0

Factor a trinomial.
3((-5 + -2x)(11 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
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 = {-2.5, 11}